What is the Least Common Multiple of 21112 and 21126?
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 21112 and 21126 is 31858008.
LCM(21112,21126) = 31858008
Least Common Multiple of 21112 and 21126 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21112 and 21126, than apply into the LCM equation.
GCF(21112,21126) = 14
LCM(21112,21126) = ( 21112 × 21126) / 14
LCM(21112,21126) = 446012112 / 14
LCM(21112,21126) = 31858008
Least Common Multiple (LCM) of 21112 and 21126 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21112 and 21126. First we will calculate the prime factors of 21112 and 21126.
Prime Factorization of 21112
Prime factors of 21112 are 2, 7, 13, 29. Prime factorization of 21112 in exponential form is:
21112 = 23 × 71 × 131 × 291
Prime Factorization of 21126
Prime factors of 21126 are 2, 3, 7, 503. Prime factorization of 21126 in exponential form is:
21126 = 21 × 31 × 71 × 5031
Now multiplying the highest exponent prime factors to calculate the LCM of 21112 and 21126.
LCM(21112,21126) = 23 × 71 × 131 × 291 × 31 × 5031
LCM(21112,21126) = 31858008
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