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What is the Least Common Multiple of 29950 and 29970?

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 29950 and 29970 is 89760150.

LCM(29950,29970) = 89760150

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Least Common Multiple of 29950 and 29970 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29950 and 29970, than apply into the LCM equation.

GCF(29950,29970) = 10
LCM(29950,29970) = ( 29950 × 29970) / 10
LCM(29950,29970) = 897601500 / 10
LCM(29950,29970) = 89760150

Least Common Multiple (LCM) of 29950 and 29970 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29950 and 29970. First we will calculate the prime factors of 29950 and 29970.

Prime Factorization of 29950

Prime factors of 29950 are 2, 5, 599. Prime factorization of 29950 in exponential form is:

29950 = 21 × 52 × 5991

Prime Factorization of 29970

Prime factors of 29970 are 2, 3, 5, 37. Prime factorization of 29970 in exponential form is:

29970 = 21 × 34 × 51 × 371

Now multiplying the highest exponent prime factors to calculate the LCM of 29950 and 29970.

LCM(29950,29970) = 21 × 52 × 5991 × 34 × 371
LCM(29950,29970) = 89760150