A jar contains a large number of pennies. The pennies can be divided into equal shares among 3, 4, 5, 6, 7, or 8 children with no pennies left over each time. What is the least number of pennies the jar could contain?
To find the least number of pennies the jar could contain, we need to find the lowest common multiple (LCM) of the numbers 3, 4, 5, 6, 7, and 8.
Step 1:
First, list out the prime factors for each number:
3 = 3
4 = 2^2
5 = 5
6 = 2 * 3
7 = 7
8 = 2^3
Step 2:
Identify the highest power of each prime factor:
2^3 x 3 x 5 x 7
Step 3:
Multiply the prime factors to get the LCM:
2^3 x 3 x 5 x 7 = 840
Therefore, the least number of pennies the jar could contain is 840.
it must contain all the prime factors of these numbers, so
2^3 * 3 * 5 * 7 = ______