# Getting the Least Common Multiple

The most common solution to this question which was given during the 1^{st} Math2Shine International Vedic Mathematics Competition held last July 2023, is “prime Factorization method”. For this we would need paper and pencil to make our computations.

2 | 132 308

2 | 66 154

11| 33 77

3 7

HCF = 2 x 2 x 11 = 48

LCM = 2 x 2 x 11 x 3 x 7 = HCF x 3 x 7 = 924.

But knowledge of divisibility tests and vertically and crosswise can help us find the correct answer mentally. If we look at the numbers 132 and 308, we can quickly notice that both are divisible by 4 → 32 and 08 are divisible by 4 and by 11 → (1 + 2) – 3 = 0 and (3 + 8) – 0 = 11.

So, we can say that 4 x 11 = 44 is a factor of the two numbers. But dividing by 44 may be difficult so we can divide the two numbers by 11 first to get 12 and 28. We then divide them by 4 to get 3 and 7.

Now it is easy to multiply crosswise, 308 by 3 to get 924, the LCM. To verify, we can also multiply 132 by 7 and see that it also gives 924.

The method we described is also far easier than using the relation 132 x 308 = HCF x LCM or LCM = (132 x 308)/48.