What is the Least Common Multiple of 19824 and 19838?
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 19824 and 19838 is 28090608.
LCM(19824,19838) = 28090608
Least Common Multiple of 19824 and 19838 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 19824 and 19838, than apply into the LCM equation.
GCF(19824,19838) = 14
LCM(19824,19838) = ( 19824 × 19838) / 14
LCM(19824,19838) = 393268512 / 14
LCM(19824,19838) = 28090608
Least Common Multiple (LCM) of 19824 and 19838 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 19824 and 19838. First we will calculate the prime factors of 19824 and 19838.
Prime Factorization of 19824
Prime factors of 19824 are 2, 3, 7, 59. Prime factorization of 19824 in exponential form is:
19824 = 24 × 31 × 71 × 591
Prime Factorization of 19838
Prime factors of 19838 are 2, 7, 13, 109. Prime factorization of 19838 in exponential form is:
19838 = 21 × 71 × 131 × 1091
Now multiplying the highest exponent prime factors to calculate the LCM of 19824 and 19838.
LCM(19824,19838) = 24 × 31 × 71 × 591 × 131 × 1091
LCM(19824,19838) = 28090608
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