Question

# A number is divisible by both $5$ and $12$. By which another number will that number be always divisible?

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Solution

## Given that a number is divisible by both $5$ and $12$.We have to find another number by which the given number is always divisible.We know thatFactors of $5$ are $1,5$Factors of $12$ are $1,2,3,4,6,12$Since $5$ and $12$ have no common factor other than $1$, therefore they are co-primes and we know that if a number is divisible by two co-primes, then it is also divisible by their product.The product of $5$ and $12$ $=5×12=60$. Thus the number is always divisible by $60$. Therefore, if a number is divisible by both $5$ and $12$, it will be divisible by $60$.

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