Question

# Given H.C.F of 306 and 1314 is 18. Find their L.C.M.

Hint: We know that the product of two numbers is equal to the product of their HCF and LCM.We have to use the formula, $a\text{ x }b\text{ }=\text{ }HCF\text{ x }LCM.$

So here we are given two numbers 306 and 1314. The HCF (Highest Common Factor) of the numbers is 18. We need to find the LCM (Lowest common multiple) of 306 and 1314.
We know a relation between two numbers and their LCM and HCF, that is
Product of H.C.F and L.C.M = Product of two numbers
H.C.F x L.C.M = a x b …. (i)
We already know the two numbers and their H.C.F, to find the L.C.M, we have to put the values in equation (i).
We get,
18 x L.C.M = 306 x 1314
L.C.M = $\dfrac{306\times1314}{18}$ …. (ii)
The common factor of 1314 and 18 is 18. So dividing the equation (ii) by 18 we get,
L.C.M = 306 x 73
L.C.M = 22,338
So, the L.C.M (Least Common Multiple) of 306 and 1314 is 22,338.

Note: The formula used in this question, the product of two numbers is equal to the product of their H.C.F and L.C.M is only valid if there are only two numbers. If there are 3 or more than 3 numbers, this equation becomes invalid.