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What is the Least Common Multiple of 1534 and 1547?

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 1534 and 1547 is 182546.

LCM(1534,1547) = 182546

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Least Common Multiple of 1534 and 1547 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1534 and 1547, than apply into the LCM equation.

GCF(1534,1547) = 13
LCM(1534,1547) = ( 1534 × 1547) / 13
LCM(1534,1547) = 2373098 / 13
LCM(1534,1547) = 182546

Least Common Multiple (LCM) of 1534 and 1547 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1534 and 1547. First we will calculate the prime factors of 1534 and 1547.

Prime Factorization of 1534

Prime factors of 1534 are 2, 13, 59. Prime factorization of 1534 in exponential form is:

1534 = 21 × 131 × 591

Prime Factorization of 1547

Prime factors of 1547 are 7, 13, 17. Prime factorization of 1547 in exponential form is:

1547 = 71 × 131 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 1534 and 1547.

LCM(1534,1547) = 21 × 131 × 591 × 71 × 171
LCM(1534,1547) = 182546