What is the Least Common Multiple of 19380 and 19392?
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 19380 and 19392 is 31318080.
LCM(19380,19392) = 31318080
Least Common Multiple of 19380 and 19392 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19380 and 19392, than apply into the LCM equation.
GCF(19380,19392) = 12
LCM(19380,19392) = ( 19380 × 19392) / 12
LCM(19380,19392) = 375816960 / 12
LCM(19380,19392) = 31318080
Least Common Multiple (LCM) of 19380 and 19392 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 19380 and 19392. First we will calculate the prime factors of 19380 and 19392.
Prime Factorization of 19380
Prime factors of 19380 are 2, 3, 5, 17, 19. Prime factorization of 19380 in exponential form is:
19380 = 22 × 31 × 51 × 171 × 191
Prime Factorization of 19392
Prime factors of 19392 are 2, 3, 101. Prime factorization of 19392 in exponential form is:
19392 = 26 × 31 × 1011
Now multiplying the highest exponent prime factors to calculate the LCM of 19380 and 19392.
LCM(19380,19392) = 26 × 31 × 51 × 171 × 191 × 1011
LCM(19380,19392) = 31318080
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