What is the Least Common Multiple of 21497 and 21504?
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 21497 and 21504 is 66038784.
LCM(21497,21504) = 66038784
Least Common Multiple of 21497 and 21504 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21497 and 21504, than apply into the LCM equation.
GCF(21497,21504) = 7
LCM(21497,21504) = ( 21497 × 21504) / 7
LCM(21497,21504) = 462271488 / 7
LCM(21497,21504) = 66038784
Least Common Multiple (LCM) of 21497 and 21504 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21497 and 21504. First we will calculate the prime factors of 21497 and 21504.
Prime Factorization of 21497
Prime factors of 21497 are 7, 37, 83. Prime factorization of 21497 in exponential form is:
21497 = 71 × 371 × 831
Prime Factorization of 21504
Prime factors of 21504 are 2, 3, 7. Prime factorization of 21504 in exponential form is:
21504 = 210 × 31 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 21497 and 21504.
LCM(21497,21504) = 71 × 371 × 831 × 210 × 31
LCM(21497,21504) = 66038784
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