Question

Find the least number which when divided by 9,12,16 and 30 leaves a remainder of 3 in each case. solve

Answer 1

Take the LCM of 9, 12, 16 and 30.

LCM ( 9, 12, 16, 30 ) = 720.

720 is the least no. that can divide these no. leaving remainder 0.

We have to find out the number that divides leaving remainder 3 in each case.
So, we add 3 to 720.

➡ 720 + 3 = 723.

Required no is 723.

Let's check this number.

➡ 723 ÷ 9 => q = 80 and r = 3

➡ 723 ÷ 12 => q = 60 and r = 3

➡ 723 ÷ 16 => q = 45 and r = 3

➡ 723 ÷ 30 => q = 24 and = r = 3

Hope it will help u !!

Answer 2

Answer:

Concept:

Highest common factor(HCM)

Least common multiple(LCM)

Step-by-step explanation:

Given:

numbers which are divided by = 9,12,16,30

remainder = 3

Find:

The least common multiple

Solution:

9=3×3

12=3×2×2

16=2×2×2×2

30=3×5×2

LCM = 2×3×2×3×1×4×5=720

∴ required number=720+3=723

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