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HCF or Highest Common Factor (a.k.a Greatest common factor) refers to a set of two or more different numbers that can be divided by exactly or a common number. HCF is also called as GCD/GCM – Greatest Common Divisor, Greatest common denominator, or Greatest Common Factor.

LCM or Least Common Multiple refers to the smallest quantity of number that is divisible by two or more given quantities of number without a remainder: 12is the least common multiple of 2, 3, 4, and 6. LCM is also called as Lowest Common Multiple. LCM is the smallest number that is multiple of two or more numbers.

HCF and LCM are calculated by either factorization method or division method.

HCF and LCM Calculator

Table of Contents:

**Formula**

**If number ‘a’ divided another number ‘b’ exactly, then we say that ‘a’ is a factor of ‘b’.**

**In this case, ‘b’ is called a multiple of ‘a’.**

GCF - Greatest common factor can be calculated by any of the following methods,

__Factorization Method:__

Express each one of the numbers as product of prime factors.

The product of least powers of common prime factors gives HCF.

__(Greatest common divisor) Division Method:__

Two find the HCF of two given numbers, divide the largest by the small number, then divide the dividend by the remainder. Repeat this until remainder is 0. The last dividend is the HCF of the two numbers.

Least Commmon Factor(LCF) can be calculated by the following method,

__Factorization Method:__

Express each one of the numbers as product of prime factors.

The product of highest powers of all prime factors gives LCF.

__ Example__:

**Calculate the HCF (GCF or GCD) and LCM for the given set of numbers.**

Greatest Common Factor of 18,36,72

__ Solution__:

*Step1***:** Express the numbers as product of prime factors.

18 = 2× 3^{2}

36 = 2^{2} × 3^{2}

72 = 2^{3} × 3^{2}

**Step2****:** Take the prime numbers with least power and is present in all sets.

2 and 3 are the prime number common to all given numbers.

The least power of 2 in the set is - 2

The least power of 3 in the set is - 3^{2}

__ Step3:__ Product of the numbers taken.

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Least Common Multiple or Factor of 36, 90, 72.

36 = 2

90 = 2 × 5 × 3

72 = 2

2, 3,5 are the prime number identified.

The highest power of 2 in the set is - 2

The highest power of 3 in the set is - 3

The highest power of 5 in the set is - 5

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