when jason arranges his toy soldiers in rows of 6, he has left 1.when he arrahges them in rows of 8, he has 3 left over. when he arrenges in rowsof 10 then 5 left over. what is the smallest possible number of toy soldiers that jason plays with/
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To find the smallest possible number of toy soldiers that Jason plays with, we need to find the least common multiple (LCM) of the numbers 6, 8, and 10. The LCM is the smallest positive integer that is divisible by all three numbers.
One approach is to list the multiples of each number until you find a common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, ...
Multiples of 10: 10, 20, 30, 40, 50, ...
From the lists, we can see that the smallest common multiple (LCM) is 24. This means that Jason has a minimum of 24 toy soldiers to play with.
We can also use the prime factorization method to find the LCM:
Prime factors of 6: 2 × 3
Prime factors of 8: 2³
Prime factors of 10: 2 × 5
To find the LCM, we take the highest power of each prime factor:
LCM = 2³ × 3 × 5 = 24
Therefore, the smallest possible number of toy soldiers that Jason plays with is 24.