LCM - Least Common Multiple

Common multiple of a, b = Multiple of both a and b LCM of a, b = Least among the common multiples of a and b

Method of finding LCM

LCM = common factor x product of remaining factors

Ex : Find the LCM of 90 and 105 ? Write the numbers as product of factors 90 = 3 x 30 = 3 x 5 x 6 105 = 3 x 35 = 3 x 5 x 7 (Observe the common factor of the given numbers) 3 x 5 is the common factor (Make sure the remaining factors doesn't have any common factors other than 1) 6, 7 doesn’t have any common factor other than 1 LCM of 90, 105 = 3 x 5 x 6 x 7 = 15 x 6 x 7 = 90 x 7 = 630

Divisible by ‘a’

If a number is divisible by ‘a’, then the number is a Multiple of ‘a’

Ex: Numbers divisible by 4 are 4, 8, 12, 16,.... which are multiples of 4

A number divisible by both a and b = Common Multiple of a and b

Ex: Numbers which are divisible by both 4 and 6 are 12, 24, 36…. (Common multiples of 4 and 6)

**Smallest number** divisible by both a and b = **LCM** of a and b

Ex: Find the smallest number divisible by 3 and 5 ? Number divisible by 3 and 5 = Common multiple of 3 and 5 Smallest number divisible by 3 and 5 = Smallest number among common multiples of 3 and 5 = Least common multiple of 3 and 5 = LCM of 3 and 5 = 3 x 5 = 15