the number between 22000 and 23000 that is divisible by each 12,18,21 and 32
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Answer:LCM of {12,18,21,32} = 2016
Therefore, answer is 2016 x 2 = 4032
Step-by-step explanation:
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The number between 22000 and 23000 that is divisible by each 12,18,21 and 32 = 22176
Step-by-step explanation:
We have,
12, 18, 21 and 32
The number between 22000 and 23000 that is divisible by each 12, 18, 21 and 32 = ?
The LCM of 12, 18, 21 and 32
12 = 2 × 2 × 3
18 = 2 × 3 × 3
21 = 3 × 7 and
32 = 2 × 2 × 2 × 2 × 2
The LCM of 12, 18, 21 and 32 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7
= 2016
∴ The LCM of 12, 18, 21 and 32 = 2016K
Put K = 1, 2, 3, 4, 5, 6, .........
The numbers are:
2016, 4032, 6048, 8064, 10080, 12096, 14112, 16128, 18144, 20160, 22176, 24192
∴ The number between 22000 and 23000 that is divisible by each 12,18,21 and 32 = 22176
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