Jagat has a jar of different coloured marbles. He is using them to make packs of marbles such that each pack has 12 red, 15 blue and 9 green marbles. After making packs, there are no marbles left in the jar. What is the least possible number of marbles that could be in the jar at the beginning?
2 points
12
180
360
3
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Question ⤵️
Jagat has a jar of different coloured marbles. He is using them to make packs of marbles such that each pack has 12 red, 15 blue and 9 green marbles. After making packs, there are no marbles left in the jar. What is the least possible number of marbles that could be in the jar at the beginning?
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3
Answer:
The least possible number of marbles that could be in the jar at the beginning is 180.
Step-by-step explanation:
Given: Jagat has a jar of coloured marbles. It is to be packed each as 12 red,15 blue and 9 green marbles.
To find: The least possible number of marbles that could be in the jar at the beginning.
Solution: We need to take the LCM of the three marbles.
LCMis the least common multiples.
Using Prime Factorisation method , LCM is the product of all prime factors with the highest degree.
After prime factorisation we get
9= 3×3,
12= 3×2×2
15= 3×5
LCM(12,15,9) = 2×2×3×3×5=180.
Therefore the least possible number of marbles that could be in the jar at the beginning is 180 .
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