What is the Least Common Multiple of 21920 and 21930?
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 21920 and 21930 is 48070560.
LCM(21920,21930) = 48070560
Least Common Multiple of 21920 and 21930 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21920 and 21930, than apply into the LCM equation.
GCF(21920,21930) = 10
LCM(21920,21930) = ( 21920 × 21930) / 10
LCM(21920,21930) = 480705600 / 10
LCM(21920,21930) = 48070560
Least Common Multiple (LCM) of 21920 and 21930 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 21920 and 21930. First we will calculate the prime factors of 21920 and 21930.
Prime Factorization of 21920
Prime factors of 21920 are 2, 5, 137. Prime factorization of 21920 in exponential form is:
21920 = 25 × 51 × 1371
Prime Factorization of 21930
Prime factors of 21930 are 2, 3, 5, 17, 43. Prime factorization of 21930 in exponential form is:
21930 = 21 × 31 × 51 × 171 × 431
Now multiplying the highest exponent prime factors to calculate the LCM of 21920 and 21930.
LCM(21920,21930) = 25 × 51 × 1371 × 31 × 171 × 431
LCM(21920,21930) = 48070560
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