lcm of 16a and 14ab

Question

Find the LCM of 16a and 14ab?.....

Answer 1

Factorise each expression:

16a=2⁴×a, so factors are 2, 2, 2, 2, a

14ab=2×7×a×b, so factors are 2, 7, a, b

So put together the whole set of factors: 2, 2, 2, 2, 7, a, b (without repeating factors which are common).

Multiply these 112ab. This is the LCM, because 112ab/16a=7b and 112ab/14ab=8, that is, both expressions are factors of the LCM, and the individual divisors have no common factors, so 112ab is the smallest common multiple.