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What is the Least Common Multiple of 55770 and 55780?

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 55770 and 55780 is 311085060.

LCM(55770,55780) = 311085060

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Least Common Multiple of 55770 and 55780 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 55770 and 55780, than apply into the LCM equation.

GCF(55770,55780) = 10
LCM(55770,55780) = ( 55770 × 55780) / 10
LCM(55770,55780) = 3110850600 / 10
LCM(55770,55780) = 311085060

Least Common Multiple (LCM) of 55770 and 55780 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 55770 and 55780. First we will calculate the prime factors of 55770 and 55780.

Prime Factorization of 55770

Prime factors of 55770 are 2, 3, 5, 11, 13. Prime factorization of 55770 in exponential form is:

55770 = 21 × 31 × 51 × 111 × 132

Prime Factorization of 55780

Prime factors of 55780 are 2, 5, 2789. Prime factorization of 55780 in exponential form is:

55780 = 22 × 51 × 27891

Now multiplying the highest exponent prime factors to calculate the LCM of 55770 and 55780.

LCM(55770,55780) = 22 × 31 × 51 × 111 × 132 × 27891
LCM(55770,55780) = 311085060