BY Team Aakash Byju's

Step-By-Step Guide to Solve HCF and LCM Questions

Factor

If a number ‘a' divides another number 'b' exactly with a quotient y, we say that ‘a’ and 'b' are factors of ‘y’ and are represented as a/b.

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The product of a number and counting numbers are known as the multiples of that number.

Multiple

Note The number of multiples of a given number is infinite.

The highest common factor of two or more numbers is the highest common factor (H.C.F).

Highest Common Factor (H.C.F)

1. By writing all factors 2. By prime factorization method 3. By division method.

H.C.F can be determined by three methods.

Note: Another name for H.C.F is Greatest common divisor (G.C.D)

Finding H.C.F by Writing the Factors

Find H.C.F of 36, 48, and 64.

Example

H.C.F by Prime Factorization Method

Find H.C.F of 48, 52.

Example

H.C.F by Division Method

Find H.C.F of 130 and 150.

Example

Least Common Multiple (L.C.M)

The least common multiple of two or more natural numbers is the least natural multiple of the given numbers.

L.C.M can be determined by 3 methods

1. By writing the   multiples of given   numbers 2. By prime    factorization    method. 3. By division method.

Finding L.C.M by writing the multiples of given numbers

Find L.C.M of 2 and 3.

Example

Finding L.C.M by prime factorization method

Find L.C.M of 32, 48 and 72.

Example

Finding L.C.M by prime factorization method

Find L.C.M of 30, 60 and 90

Example