Page 28 - NUMINO TG_6A
P. 28
01What Do We Have in Common? Unit
2 . Solve each word problem using the least common multiple. 2. Find the LCM for each word problem.
a. Starting from the same point, black dots are marked every 6 cm, and 2b.
red dots are marked every 8 cm on a straight line. How many Understand the Question
centimeters are the black and red dots away from the starting point Q: What do you need to find?
A: The smallest number that when divided
when they are first marked at the same point? by 15 and 18 has a remainder of 2.
Q: Read the problem again. What do you
268 2 3 4 = 24 24 cm already know?
34 A: The LCM of 15 and 18 has a remainder
of 0.
The LCM of 6 and 8 is 24. Plan the Process
Q: How will you solve the problem?
b. A number has a remainder of 2 when it is divided by 15. Also, it has a A: Get the prime factors of 15 and 18, find
remainder of 2 when it is divided by 18. the LCM, and add 2.
Solve the Problem
Find the smallest possible number. 15 5 3, 18 2 3 3
LCM 5 3 2 3 90
15 = 2 90 2 92
18 = Look Back
2 Q: Does your answer make sense?
The LCM of 15 and 18 is 90.
The smallest possible number is 92.
c. Bus A comes every 4 minutes, bus B comes every 6 minutes, and bus
C comes every 12 minutes to the bus station. If all three buses come
to the station at 8:00 A.M., when will all three buses be at the bus
station again? 4 3 1 2 1 = 12 8:12 A.M.
4 4 6 12
3163
121
The LCM of 4, 6 and 12 is 12.
d. A number has a remainder of 3 when it is divided by 8, 12, and 16.
Find the smallest possible number.
8= 3
12 =
16 = 3
3
The LCM of 8, 12 and 16 is 48.
The smallest possible number is 51.
1. What Do We Have in Common? 9
Although the lowest common multiple typically refers to integers, it may refer to any rational number.
Example: What is the lowest common multiple of 4 and 2 .
5 3
Step 1: Find the smallest integer that is a multiple of 4 and 2 .
5 3
4
Step 2: List the multiples of 5 .
4 , 8 , 12 , 16 , 20 4
5 5 5 5 5
Step 3: List the multiples of 2 .
3
2 , 4 , 9 , 12 4
3 3 3 3
6A Unit 01 011
2 . Solve each word problem using the least common multiple. 2. Find the LCM for each word problem.
a. Starting from the same point, black dots are marked every 6 cm, and 2b.
red dots are marked every 8 cm on a straight line. How many Understand the Question
centimeters are the black and red dots away from the starting point Q: What do you need to find?
A: The smallest number that when divided
when they are first marked at the same point? by 15 and 18 has a remainder of 2.
Q: Read the problem again. What do you
268 2 3 4 = 24 24 cm already know?
34 A: The LCM of 15 and 18 has a remainder
of 0.
The LCM of 6 and 8 is 24. Plan the Process
Q: How will you solve the problem?
b. A number has a remainder of 2 when it is divided by 15. Also, it has a A: Get the prime factors of 15 and 18, find
remainder of 2 when it is divided by 18. the LCM, and add 2.
Solve the Problem
Find the smallest possible number. 15 5 3, 18 2 3 3
LCM 5 3 2 3 90
15 = 2 90 2 92
18 = Look Back
2 Q: Does your answer make sense?
The LCM of 15 and 18 is 90.
The smallest possible number is 92.
c. Bus A comes every 4 minutes, bus B comes every 6 minutes, and bus
C comes every 12 minutes to the bus station. If all three buses come
to the station at 8:00 A.M., when will all three buses be at the bus
station again? 4 3 1 2 1 = 12 8:12 A.M.
4 4 6 12
3163
121
The LCM of 4, 6 and 12 is 12.
d. A number has a remainder of 3 when it is divided by 8, 12, and 16.
Find the smallest possible number.
8= 3
12 =
16 = 3
3
The LCM of 8, 12 and 16 is 48.
The smallest possible number is 51.
1. What Do We Have in Common? 9
Although the lowest common multiple typically refers to integers, it may refer to any rational number.
Example: What is the lowest common multiple of 4 and 2 .
5 3
Step 1: Find the smallest integer that is a multiple of 4 and 2 .
5 3
4
Step 2: List the multiples of 5 .
4 , 8 , 12 , 16 , 20 4
5 5 5 5 5
Step 3: List the multiples of 2 .
3
2 , 4 , 9 , 12 4
3 3 3 3
6A Unit 01 011
