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What is the Least Common Multiple of 20972 and 20980?

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 20972 and 20980 is 109998140.

LCM(20972,20980) = 109998140

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Least Common Multiple of 20972 and 20980 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20972 and 20980, than apply into the LCM equation.

GCF(20972,20980) = 4
LCM(20972,20980) = ( 20972 × 20980) / 4
LCM(20972,20980) = 439992560 / 4
LCM(20972,20980) = 109998140

Least Common Multiple (LCM) of 20972 and 20980 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 20972 and 20980. First we will calculate the prime factors of 20972 and 20980.

Prime Factorization of 20972

Prime factors of 20972 are 2, 7, 107. Prime factorization of 20972 in exponential form is:

20972 = 22 × 72 × 1071

Prime Factorization of 20980

Prime factors of 20980 are 2, 5, 1049. Prime factorization of 20980 in exponential form is:

20980 = 22 × 51 × 10491

Now multiplying the highest exponent prime factors to calculate the LCM of 20972 and 20980.

LCM(20972,20980) = 22 × 72 × 1071 × 51 × 10491
LCM(20972,20980) = 109998140