while arrenging oranges in heaps of 24, 32 and 48 a fruit vendor notices that 8 oranges are always left. what is the smallest no. of orrange he has?
Answers
We substract 8 form 24 ,48 ,32 Then find lcm so lcm is 2×2×2×2×3×5=240 answer.
The smallest number of orange he has is 240
Solution:
Give that,
While arranging oranges in heaps of 24, 32 and 48 a fruit vendor notices that 8 oranges are always left
Subtract 8
24 - 8 = 16
32 - 8 = 24
48 - 8 = 40
The smallest number of oranges he has is the least common multiple of 16, 24 and 40
Find LCM of 16, 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 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, 5
Multiply these factors together to find the LCM
LCM = 2 x 2 x 2 x 2 x 3 x 5 = 240
Thus the smallest number of orange he has is 240
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