The LCM (5 and 9,610) = ? Calculate the Least (the Lowest) Common Multiple, LCM, by Using Two Methods: 1) Numbers' Divisibility and 2) The Prime Factorization

A number 'a' is divisible by a number 'b' if there is no remainder when 'a' is divided by 'b'.

Divide the larger number by the smaller one.

When we divide our numbers, there is no remainder:

9,610 ÷ 5 = 1,922 + 0

⇒ 9,610 = 5 × 1,922

⇒ 9,610 is divisible by 5.

⇒ 9,610 is a multiple of 5.

The smallest multiple of 9,610 is the number itself: 9,610.

» Online calculator. The divisibility of numbers

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

5 is a prime number, it cannot be broken down into other prime factors.

9,610 = 2 × 5 × 31²
9,610 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* Prime number: a natural number that is only divisible by 1 and itself. A prime number has exactly two factors: 1 and itself.
* Composite number: a natural number that has at least one other factor than 1 and itself.

Multiply all the prime factors of the two numbers. If there are common prime factors then only the ones with the largest exponents are taken (the largest powers).

Why is it useful to calculate the least common multiple?

In order to add, subtract or sort fractions with different denominators, we must make their denominators the same. An easy way is to calculate the least common multiple of all the denominators (the least common denominator).

By definition, the least common multiple of two numbers is the smallest natural number that is: (1) greater than 0 and (2) a multiple of both numbers.