Answer:
72
Step-by-step explanation:
The smallest number that is divisible by two given numbers is called the Least Common Multiple (LCM) of those numbers.
What's the smallest number that is a multiple of 8 and also a multiple of 18?
One way to find out is to start making lists of multiples:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, and so on,
Multiples of 18: 18, 36, 54, 72, 90, 108, and so on.
This method can be a bit tedious, but in this case, it's clear that 72 is the LCM of 8 and 18.
Another method is to use the <u>prime factorization</u> of the two numbers.
Write 8 and 18 as the product of prime numbers; each number has a unique prime factorization.
8 = 2 x 2 x 2 = 2^3
18 = 2 x 3 x 3 = 2^1 x 3^2
To form the LCM, build a product of primes using the <u>highest exponent</u> in either of the two numbers.
LCM = 2^3 x 3^2 = 8 x 9 = 72.
