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When you go to a baseball game, you’ll notice that all the players all have numbers on the backs of their uniforms so that you can tell who is who–20, 38, 87.
Suppose you saw two players numbers and asked wanted to know what numbers were divisible by both numbers. Is it starting to sound like math class?
So here’s a common problem that you will find on standardized tests that you can practice the next time you go to the old ballgame.
All numbers divisible by 20 and 13 are also divisible by which of the following?
A. 99
B. 146
C. 128
D. 26
E. 154
The way to solve this problem is to first write the prime factorization of each number
20 = 2 x 10 = 2 x 2 x 5
13 = 1 x 13
Notice that 13 is a prime number with only the factors 1 and 13. Next write the prime factorization of the Least Common Multiple (LCM)
LCM(20,13) = 2 x 2 x 5 x 13
Any number that is divisible by both 20 and 13 will also be divisible by any combination of the prime factors of the LCM(20,13). For example,
2 x 2 = 4
2 x 5 = 10
1 x 13 = 13
2 x 2 x 5 = 20
2 x 13 = 26
The only choice that satisfies this is D. 26 which can be written as 2 x 13 = 26
Watch the presentation Common Divisibility Examples at Khan Academy.
