Which of the following is false?
a. A number that is divisible by 3 and 20 is divisible by 60.
b. A number that is divisible by 4 and 15 is divisible by 60.
c. A number that is divisible by 5 and 12 is divisible by 60.
d. A number that is divisible by 6 and 10 is divisible by 60.
letter D is false.
For instance, 90 is divisible by 6 and 10, but not divisible by 60.
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To determine which statement is false, we need to examine each option and check if it is always true or not. Let's consider each option:
a. A number that is divisible by 3 and 20 is divisible by 60.
To answer this question, we need to find the least common multiple (LCM) of 3 and 20, which is 60. Therefore, this statement is true.
b. A number that is divisible by 4 and 15 is divisible by 60.
Again, we need to find the LCM of 4 and 15, which is 60. So this statement is also true.
c. A number that is divisible by 5 and 12 is divisible by 60.
Once again, the LCM of 5 and 12 is 60. Therefore, this statement is true as well.
d. A number that is divisible by 6 and 10 is divisible by 60.
Now, let's find the LCM of 6 and 10, which is 30. This means that 30 is the smallest number that is divisible by both 6 and 10. However, 30 is not divisible by 60. Therefore, this statement is false.
So, the false statement is option d: A number that is divisible by 6 and 10 is divisible by 60.