Page 18 - Arithmetic

LCM – Least common factor
LCM of two numbers is the smallest non-zero number which is a multiple of both. For example,
LCM of 4 and 3 is 12
Multiples of 4 = 4, 8, 12, 16....
Multiples of 3 = 3, 6, 9, 12, 15 The common multiple is 12.
Worked Example
Find the HCF of 36, 45, and 66.
36 = 2 × 2 × 3 × 3
45 = 3 × 3 × 5
66 = 2 × 3 × 11
Here, 3 is the smallest number dividing the three numbers. So, the LCM of 36, 45, and 66 is 3.
REMEMBER:
Product of two numbers = Product of the LCM and HCF Two numbers are co-prime when their HCF is 1.
HCF of fractions = 𝐻𝐶𝐹 𝑜𝑓 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝐿𝐶𝑀 𝑜𝑓 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
LCMoffractions= 𝐿𝐶𝑀𝑜𝑓𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝐻𝐶𝐹 𝑜𝑓 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
Page 17 of 55
Arithmetic Concept