Grandmother baked cookies for her grandchildren, some of whom were going to visit her that day. She wanted each of her grandchildren to have the same number of cookies, but she forgot if three, five, or six grandchildren were coming. So, she baked enough cookies so that there would be an equal number for every grandchild regardless of how many visited. Which of these could be the number of cookies Grandmother baked?A. 12B. 15C. 18D. 24
Question
Grandmother baked cookies for her grandchildren, some of whom were going to visit her that day. She wanted each of her grandchildren to have the same number of cookies, but she forgot if three, five, or six grandchildren were coming. So, she baked enough cookies so that there would be an equal number for every grandchild regardless of how many visited. Which of these could be the number of cookies Grandmother baked?A. 12B. 15C. 18D. 24
Solution
The grandmother needs to bake a number of cookies that can be evenly divided by 3, 5, and 6. This means we are looking for the least common multiple (LCM) of these numbers.
Step 1: Find the LCM of 3, 5, and 6. The LCM of 3, 5, and 6 is 30.
Step 2: Compare the LCM with the options given.
Option A: 12 - This number cannot be evenly divided by 5, so it's not a possible number of cookies.
Option B: 15 - This number cannot be evenly divided by 6, so it's not a possible number of cookies.
Option C: 18 - This number cannot be evenly divided by 5, so it's not a possible number of cookies.
Option D: 24 - This number cannot be evenly divided by 5, so it's not a possible number of cookies.
None of the given options are possible numbers of cookies the grandmother could have baked if she wanted each grandchild to have an equal number, regardless of whether 3, 5, or 6 grandchildren visited. The least number of cookies she could have baked is 30.
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