Which number is a multiple of three and a multiple of seven?
Let’s start with 18. We know that three times six equals 18, and that means 18 is a multiple of three. In order for 18 to be a multiple of seven, seven times some whole number must equal 18. Seven times two equals 14, and seven times three equals 21. There is no whole number we can multiply seven by to equal 18, and that means 18 is not a multiple of three and seven.
Next step, let’s think about three. Can the number three be a multiple of seven? Three is not a multiple of seven. What about 49? Seven times seven equals 49. Is there anything we can multiply by three to equal 49? No, 49 is not a multiple of three; it’s only a multiple of seven. What about 42? Seven times six equals 42. 42 is a multiple of seven, and six is a multiple of three. That means 42 is also divisible by three. Three times 14 equals 42, which means 42 is a multiple of three and a multiple of seven.
If you didn’t remember all of these multiplication facts, another way to find the multiples of three and seven is to list them out. Three times one is three; three times two is six; and keep going: nine, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42. And for seven, seven times one is seven; seven times two is 14, 21, 28, 35, 42. 42 is a multiple of seven and three. We also notice that 21 is a multiple of seven and three. But 21 wasn’t in our box, only 42 was, which makes our final answer 42.