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Activity 3 The Least Common Multiple
jOb ective Identify the least common multiple and relate common multiples and the least common multiple.
1. Textbook Instructions Activity 3 The Least Common Multiple
Explain the least common multiple. Have Learn about the least common multiple.
students use common multiples of two
numbers to find the least common multiple. The least common multiple (LCM) is the smallest common multiple
of two or more numbers.
Have students use a calendar to learn about Jessica and Ann are taking swimming lessons at the same sports center.
the least common multiple (LCM). Jessica takes lessons every 4 days, and Ann takes lessons every 6 days.
From February 1, Jessica receives swimming When do they take lessons together for the first time? (There is only
lessons once every four days. Ann receives one swimming lesson each day.)
swimming lessons once every six days. Find
when they will both receive swimming February
lessons. Sun Mon Tue Wed Thu Fri Sat
Have students skip-count by 4s and 123456
mark the days with circles when Jessica 7 8 9 10 11 12 13
receives her swimming lessons from 14 15 16 17 18 19 20
February 1 on the calendar. 21 22 23 24 25 26 27
Have students skip-count by 6s and 28
mark the days with triangles when Ann
receives her swimming lessons from Draw a on the dates Jessica takes lessons. February 12
February 1 on the calendar. Draw a on the dates Ann takes lessons.
The date that has both a circle and a Find the date they will take lessons together for the first time.
triangle is when both of them will receive
swimming lessons. Find the first time that Solve the problem above using the least common multiple.
both of them will receive swimming
lessons. February 12. Find the common multiples.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28 ...
Have students use what they have learned Multiples of 6: 6, 12, 18, 24, 30, 36, 42 ...
Common multiples of 4 and 6: 12, 24 ...
to find multiples, common multiples, and the
Find the smallest common multiple.
least common multiple of 4 and 6. The least common multiple: 12
Refer to . Jessica and Ann will take lessons together for the first time on February
12 .
8
2. Build Understanding
Using the Least Common Multiple to Solve a Problem.
Have students look at the calendar and see that the numbers that are skip-counted by 4s (Jessica) are multiples of
4 and the numbers that are skip-counted by 6s (Ann) are multiples of 6.
Step1: Have students use the multiplication table of 4 to find the multiples of 4 and use the multiplication table of 6 to
find the multiples of 6.
Step2: Have them mark common numbers among the multiples. The marked numbers are common multiples of 4 and 6.
Step3: The smallest number out of all the common multiples (the first common multiple) is called the least common
multiple.
Step4: 12 is the least common multiple of 4 and 6. Jessica and Ann will take lessons together for the first time on
February 12.
010 NUMINO Teacher s Guide
jOb ective Identify the least common multiple and relate common multiples and the least common multiple.
1. Textbook Instructions Activity 3 The Least Common Multiple
Explain the least common multiple. Have Learn about the least common multiple.
students use common multiples of two
numbers to find the least common multiple. The least common multiple (LCM) is the smallest common multiple
of two or more numbers.
Have students use a calendar to learn about Jessica and Ann are taking swimming lessons at the same sports center.
the least common multiple (LCM). Jessica takes lessons every 4 days, and Ann takes lessons every 6 days.
From February 1, Jessica receives swimming When do they take lessons together for the first time? (There is only
lessons once every four days. Ann receives one swimming lesson each day.)
swimming lessons once every six days. Find
when they will both receive swimming February
lessons. Sun Mon Tue Wed Thu Fri Sat
Have students skip-count by 4s and 123456
mark the days with circles when Jessica 7 8 9 10 11 12 13
receives her swimming lessons from 14 15 16 17 18 19 20
February 1 on the calendar. 21 22 23 24 25 26 27
Have students skip-count by 6s and 28
mark the days with triangles when Ann
receives her swimming lessons from Draw a on the dates Jessica takes lessons. February 12
February 1 on the calendar. Draw a on the dates Ann takes lessons.
The date that has both a circle and a Find the date they will take lessons together for the first time.
triangle is when both of them will receive
swimming lessons. Find the first time that Solve the problem above using the least common multiple.
both of them will receive swimming
lessons. February 12. Find the common multiples.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28 ...
Have students use what they have learned Multiples of 6: 6, 12, 18, 24, 30, 36, 42 ...
Common multiples of 4 and 6: 12, 24 ...
to find multiples, common multiples, and the
Find the smallest common multiple.
least common multiple of 4 and 6. The least common multiple: 12
Refer to . Jessica and Ann will take lessons together for the first time on February
12 .
8
2. Build Understanding
Using the Least Common Multiple to Solve a Problem.
Have students look at the calendar and see that the numbers that are skip-counted by 4s (Jessica) are multiples of
4 and the numbers that are skip-counted by 6s (Ann) are multiples of 6.
Step1: Have students use the multiplication table of 4 to find the multiples of 4 and use the multiplication table of 6 to
find the multiples of 6.
Step2: Have them mark common numbers among the multiples. The marked numbers are common multiples of 4 and 6.
Step3: The smallest number out of all the common multiples (the first common multiple) is called the least common
multiple.
Step4: 12 is the least common multiple of 4 and 6. Jessica and Ann will take lessons together for the first time on
February 12.
010 NUMINO Teacher s Guide
