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What is the Least Common Multiple of 67569 and 67580?

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 67569 and 67580 is 4566313020.

LCM(67569,67580) = 4566313020

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Least Common Multiple of 67569 and 67580 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 67569 and 67580, than apply into the LCM equation.

GCF(67569,67580) = 1
LCM(67569,67580) = ( 67569 × 67580) / 1
LCM(67569,67580) = 4566313020 / 1
LCM(67569,67580) = 4566313020

Least Common Multiple (LCM) of 67569 and 67580 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 67569 and 67580. First we will calculate the prime factors of 67569 and 67580.

Prime Factorization of 67569

Prime factors of 67569 are 3, 101, 223. Prime factorization of 67569 in exponential form is:

67569 = 31 × 1011 × 2231

Prime Factorization of 67580

Prime factors of 67580 are 2, 5, 31, 109. Prime factorization of 67580 in exponential form is:

67580 = 22 × 51 × 311 × 1091

Now multiplying the highest exponent prime factors to calculate the LCM of 67569 and 67580.

LCM(67569,67580) = 31 × 1011 × 2231 × 22 × 51 × 311 × 1091
LCM(67569,67580) = 4566313020