Find the least number which when added to 7 becomes exactly divisible by 16 18 24 and 40
Answers
713 is the least number which when added to 7 becomes exactly divisible by 16 18 24 and 40
Solution:
Find the least common multiple of 16 18 24 and 40
List all prime factors for each number.
Prime Factorization of 16 is: 2 x 2 x 2 x 2
Prime Factorization of 18 is: 2 x 3 x 3
Prime Factorization of 24 is: 2 x 2 x 2 x 3
Prime Factorization of 40 is: 2 x 2 x 2 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
2, 2, 2, 2, 3, 3, 5
Multiply these factors together to find the LCM
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720
Thus the least number is: 720 - 7 = 713
Hence the least number which when added to 7 becomes exactly divisible by 16 18 24 and 40 is 713
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first of all we should find the prime factors of all numbers which is exactly divisible
prime factor of 16 is 2×2×2×2
prime factor of 18 is2×3×3
prime factor of 24 is 2×2×2×3
prime factors of 40 is 2×2×2×5
now remove the LCM 2×2×2×2×3×3×5= 720
now remove 7 from 720
720-7=713
713 is the answer