Question

Find the LCM of the following numbers:

(a) 9 and 4 (b) 12 and 5

(c) 6 and 5 (d) 15 and 4

Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?

Answer 1

(a)

2	9, 4
2	9, 2
3	9, 1
3	3, 1
	1, 1

LCM = 2 × 2 × 3 × 3 = 36

(b)

2	12, 5
2	6, 5
3	3, 5
5	1, 5
	1, 1

LCM = 2 × 2 × 3 × 5 = 60

(c)

2	6, 5
3	3, 5
5	1, 5
	1, 1

LCM = 2 × 3 × 5 = 30

(d)

2	15, 4
2	15, 2
3	15, 1
5	5, 1
	1, 1

LCM = 2 × 2 × 3 × 5 = 60

Yes, it can be observed that in each case, the LCM of the given numbers is the product of these numbers. When two numbers are co-prime, their LCM is the product of those numbers. Also, in each case, LCM is a multiple of 3.