Find the smallest number which when divided by 6,8,12,15 and 20 leaves the same remainder 5.
Answers
6=2×3
8=2×2×2
12=2×2×3
15=3×5
20=2×2×5
LCM=2×2×2×3×5
=120
So the smallest number is 120+5=125
Answer:
The smallest number which when divided by 6,8,12,15 and 20 and leaves the remainder 5 = 125
Step-by-step explanation:
To find,
Find the smallest number which when divided by 6,8,12,15 and 20 leaves the same remainder 5.
Solution:
The least number which when divided by the given numbers and leaves no reminder is the LCM of the numbers
The smallest number which when divided by 6,8,12,15 and 20 leaves no remainder is the LCM of 6,8,12,15 and 20
Hence the smallest number which when divided by 6,8,12,15 and 20 and leaves remainder 5 = LCM(6,8,12,15,20) + 5
To find the LCM(6,8,12,15,20)
The prime factorization of 6 = 2×3
The prime factorization of 8 = 2×2×2
The prime factorization of 12 = 2×2×3
The prime factorization of 15 = 3×5
The prime factorization of 20 = 2×2×5
LCM(6,8,12,15,20) = 2×2×2×3×5 = 120
The smallest number which when divided by 6,8,12,15 and 20 and leaves remainder 5 = LCM(6,8,12,15,20) + 5
= 120 +5
= 125
∴The smallest number which when divided by 6,8,12,15 and 20 and leaves the remainder 5 = 125
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