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What is the Least Common Multiple of 21400 and 21417?

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 21400 and 21417 is 458323800.

LCM(21400,21417) = 458323800

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Least Common Multiple of 21400 and 21417 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21400 and 21417, than apply into the LCM equation.

GCF(21400,21417) = 1
LCM(21400,21417) = ( 21400 × 21417) / 1
LCM(21400,21417) = 458323800 / 1
LCM(21400,21417) = 458323800

Least Common Multiple (LCM) of 21400 and 21417 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21400 and 21417. First we will calculate the prime factors of 21400 and 21417.

Prime Factorization of 21400

Prime factors of 21400 are 2, 5, 107. Prime factorization of 21400 in exponential form is:

21400 = 23 × 52 × 1071

Prime Factorization of 21417

Prime factors of 21417 are 3, 11, 59. Prime factorization of 21417 in exponential form is:

21417 = 31 × 112 × 591

Now multiplying the highest exponent prime factors to calculate the LCM of 21400 and 21417.

LCM(21400,21417) = 23 × 52 × 1071 × 31 × 112 × 591
LCM(21400,21417) = 458323800