# What is the Least Common Multiple of 84 and 103?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 84 and 103 is 8652.

LCM(84,103) = 8652

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## Least Common Multiple of 84 and 103 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 103, than apply into the LCM equation.

GCF(84,103) = 1
LCM(84,103) = ( 84 × 103) / 1
LCM(84,103) = 8652 / 1
LCM(84,103) = 8652

## Least Common Multiple (LCM) of 84 and 103 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 84 and 103. First we will calculate the prime factors of 84 and 103.

### Prime Factorization of 84

Prime factors of 84 are 2, 3, 7. Prime factorization of 84 in exponential form is:

84 = 22 × 31 × 71

### Prime Factorization of 103

Prime factors of 103 are 103. Prime factorization of 103 in exponential form is:

103 = 1031

Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 103.

LCM(84,103) = 22 × 31 × 71 × 1031
LCM(84,103) = 8652