Question

To find the least common multiple of pair of numbers, 60, 72 using prime factorsmethod.

Factors and multiples
ANSWERED
asked 2021-08-06
To find the least common multiple of pair of numbers, 60, 72 using prime factorsmethod.

Answers (1)

2021-08-07
Given pair of numbers: 60,72.
Concept used:
Least common multiple of two or more numbers is the smallest multiple that is completely divisible by the corresponding numbers leaving remainder zero. Least Common Multiple (LCM) can be find by two methods - one by multiples method while other by prime factors method.
In multiples method, we list out multiples of given numbers and look out for the least multiple that is common for all the given numbers. In case, we don't find any of common multiple then we simply multiple the given numbers, the product obtained is the least common multiple of the given numbers.
In prime factors method, we break the given numbers in terms of their prime factors and look out for common factors. Then, we multiply the each of the common factor, number of times it occurs in factorization of any of the number and the factors that are not common. The product thus, obtained is the least common multiple of the given numbers.
Calculations:
According to question, the given pair of numbers are 60, 72.
Using prime factors method, we have,
\(\displaystyle\Rightarrow{60}={2}\times{2}\times{2}\times{5}\)
\(\displaystyle\Rightarrow{72}={2}\times{2}\times{2}\times{3}\times{3}\)
From the above, we find that the common factor among factors of 60, 72 are 2, 2 and 2 and uncommon factors are 3, 3 and 5. So, we have,
\(\displaystyle\Rightarrow{L}{C}{M}={2}\times{2}\times{2}\times{3}\times{3}\times{5}\) [Simplifying]
\(\displaystyle={360}\)
Hence, the least common multiple of pair of numbers 60, 72 is 360.
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