Question: Craig is thinking of a secret number. He tells his brother that it is divisible by 7 and tells his friend that it is divisible by 8. If Craig is telling the truth to both of them, what is the smallest secret number that Craig could be thinking of?
(1) 52
(2) 56
(3) 50
(4) 46
Solution:
REMEMBER : The lowest common multiple is the smallest whole number that is a multiple of each of two or more numbers.
You need to find the smallest number that is a multiple of both 7 and 8. This is the lowest common multiple.
Write the prime factorisation for each number. 7 is a prime number. You do not need to factorise 7.
7
8 = 2 × 2 × 2
Repeat each prime factor the most number of times it appears in any of the prime factorisations above.
The most the factor 2 appears is three times.
The most the factor 7 appears is once.
So, multiply:
2 × 2 × 2 × 7 = 56
The lowest common multiple of 7 and 8 is 56. That means that the smallest possible secret number is 56, because 8 times 7 is 56 and 7 times 8 is 56.
The smallest secret number that Craig could be thinking of is 56.
Then the option is (2).
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