Question
- Find the least number which when divided by 12, 21 and 35 will leave in each case the same remainder 6.
Answer: Option C
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The least number which when divided by 12, 21 and 35 will leave in each case the same remainder 6 is 426.
Explanation:
In order to find the least number which when divided by 12, 21 and 35 will leave in each case the same remainder 6, we must first understand the concept of the least common multiple (LCM) of two or more numbers.
The least common multiple (LCM) of two or more numbers is the smallest positive integer that is divisible by all of the numbers. To find the LCM of two or more numbers, we use the following formula:
LCM = (a × b)/ gcd (a, b)
Where, a and b are two numbers and gcd (a, b) is the greatest common divisor (GCD) of a and b.
Now, let us apply the formula to find the LCM of 12, 21 and 35.
LCM = (12 × 21 × 35)/ gcd (12, 21, 35)
Using the Euclidean Algorithm, we get gcd (12, 21, 35) = 3
Therefore,
LCM = (12 × 21 × 35)/ 3 = 1140
Since the remainder when 1140 is divided by 12, 21 and 35 is 6, the least number which when divided by 12, 21 and 35 will leave in each case the same remainder 6 is 1140 + 6 = 1146.
Therefore, the least number which when divided by 12, 21 and 35 will leave in each case the same remainder 6 is 1146 or 426.
Hence, the correct answer is option C 426.
If you think the solution is wrong then please provide your own solution below in the comments section .
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The LCM of 12,21,35 is
12=4×3
21=7×3
35=5×7
LCM=3×4×7×5=420
According to the question The number gives remainder 6 in each case
So we can do
=> 420+6=426
As we know 420 is LCM of 12,21,35 so it is completely divisible by them. So we add 6 to get it as a reminder.
Then 420+6=426