What least number is divisible by 18, 21, 24 and 30 leaves a remainder 9 ?
Answers
2529
Step-by-step explanation:
first of all find LCM of 18 21 24 30
18 = 2x3x3
24=2×2×2×3
21=3×7
30=2×3×5
LCM=2x2x3x3x5x7=2520
NOW Add 9 in LCM which is 2520+9=2529
Now
2529 18-leaving remainder 9 and quotient 13
2529-21-leaving remainder 9 and quotient 12
2529-24-leaving remainder 9 and quotient 105
2529-30-leaving remainder 9 and quotient 84
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Answer:
2884
Step-by-step explanation:
What is the least number which when divided by 12, 16, 18 and 30 leaves a remainder of 4 in each case but is completely divisible by 7?
First of all find LCM and as it leaves remainder of 4 then the number is LCM +4
12=2×2×3=2^2×3
16=2×2×2×2=2^4
18=2×3×3=3^2×2
30=2×3×5
LCM (12,16,18,30)=2^4×3^2×5
LCM=16×9×5
LCM=720
The number can be 720+4=724
But the condition is, the number should also be completely divisible by 7
As 724 is not completely divisible by 7
Therefore the number is multiple of 720 plus 4 which is divisible by 7
720×2+4=1444 not divisible by 7
720×3+4=2164 not divisible by 7
720×4+4=2884
2884 is completely divisible by 7
Answer is 2884