# If a = 2^3 × 3, b = 2 × 3 × 5, c = 3^n × 5 and LCM (a, b, c) = 2^3 × 3^2 × 5, then n =?

By Mandeep Kumar|Updated : May 24th, 2023

The value of 'n' is 2 if a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5. To determine this, candidates have to find the LCM of a, b, and c. After finding the LCM, of a, b, and c it will be easy to get the value of n.

Given: LCM (a, b, c) = 23 × 32 × 5 (equation 1)

To find: value of 'n'

a = 23 × 3, b = 2 × 3 × 5, and c = 3n × 5

We are aware that while assessing LCM, we use prime numbers with higher exponents to factor the number.

As a result, by using this formula and assuming that n is more than or equal to 1, we may calculate the LCM as

LCM (a, b, c) = 23 × 3n × 5 (equation 2)

Comparing equation 1 and equation 2, we will get

23 × 32 × 5 = 23 × 3n × 5

n = 2

Therefore, the value of n is 2.

## Value of 'n' in a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5

As discussed above, the value of n = 2 for a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5. The abbreviation "LCM" stands for "Least Common Multiple." The smallest multiple shared by two or more different numbers is referred to as the least common multiple.

When, HCF ( p, q, r) × LCM (p, q, r) is not equal to p × q × r, where p, q, r are positive integers then

LCM (p, q, r) = [p × q × r × HCF ( p, q, r)] ÷ HCF (p,q) × HCF (q,r) × HCF (p,r) and

HCF ( p, q, r) =  [p × q × r × LCM ( p, q, r)] ÷ LCM (p,q) × LCM (q,r) × LCM (p,r)

Summary:

## If a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5, then n =?

The value of n = 2 if a = 23 × 3, b = 2 × 3 × 5, c = 3n × 5 and LCM (a, b, c) = 23 × 32 × 5. To find the value of 'n' find the LCM of a, b, and c and then compare its values with LCM (a, b, c) = 23 × 32 × 5.

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