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 =?

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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