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What is the Least Common Multiple of 29953 and 29960?

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 29953 and 29960 is 128198840.

LCM(29953,29960) = 128198840

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Least Common Multiple of 29953 and 29960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29953 and 29960, than apply into the LCM equation.

GCF(29953,29960) = 7
LCM(29953,29960) = ( 29953 × 29960) / 7
LCM(29953,29960) = 897391880 / 7
LCM(29953,29960) = 128198840

Least Common Multiple (LCM) of 29953 and 29960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29953 and 29960. First we will calculate the prime factors of 29953 and 29960.

Prime Factorization of 29953

Prime factors of 29953 are 7, 11, 389. Prime factorization of 29953 in exponential form is:

29953 = 71 × 111 × 3891

Prime Factorization of 29960

Prime factors of 29960 are 2, 5, 7, 107. Prime factorization of 29960 in exponential form is:

29960 = 23 × 51 × 71 × 1071

Now multiplying the highest exponent prime factors to calculate the LCM of 29953 and 29960.

LCM(29953,29960) = 71 × 111 × 3891 × 23 × 51 × 1071
LCM(29953,29960) = 128198840