What is the Least Common Multiple of 20394 and 20414?
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 20394 and 20414 is 208161558.
LCM(20394,20414) = 208161558
Least Common Multiple of 20394 and 20414 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 20394 and 20414, than apply into the LCM equation.
GCF(20394,20414) = 2
LCM(20394,20414) = ( 20394 × 20414) / 2
LCM(20394,20414) = 416323116 / 2
LCM(20394,20414) = 208161558
Least Common Multiple (LCM) of 20394 and 20414 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 20394 and 20414. First we will calculate the prime factors of 20394 and 20414.
Prime Factorization of 20394
Prime factors of 20394 are 2, 3, 11, 103. Prime factorization of 20394 in exponential form is:
20394 = 21 × 32 × 111 × 1031
Prime Factorization of 20414
Prime factors of 20414 are 2, 59, 173. Prime factorization of 20414 in exponential form is:
20414 = 21 × 591 × 1731
Now multiplying the highest exponent prime factors to calculate the LCM of 20394 and 20414.
LCM(20394,20414) = 21 × 32 × 111 × 1031 × 591 × 1731
LCM(20394,20414) = 208161558
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