What is the smallest number ,which when divided by 7,18,56 and 36, leaves a remainder 0?
a, 390
b, 392
c, 504
d, 1012
Answers
Answer:
The answer is 504.
Step-by-step explanation:
To get to the answer, you need to compute the lowest common multiple (LCM) of the given numbers.
To compute the LCM, we can proceed as follows -
7=1×77=1×7
18=2×3×318=2×3×3
56=2×2×2×756=2×2×2∗7
36=2×2×3×336=2×2×3×3
Basically, I have expanded the numbers as products of prime numbers/factors (and 1 if necessary).
Now, we multiply each prime factor the greatest number of times it occurs in either number's expansion.
So we have,
LCM=2×2×2×3×3×7=504
LCM=2×2×2×3×3×7=504
Hence, the answer is 504.
Answer:
Concept:
Least common multiple (LCM) is a method to find the least common multiple between any two or more numbers. A common multiple is a number that is a multiple of two or more number.
LCM is also used to add or subtract any two fractions if the denominators of the fractions are different. When performing any arithmetic operations such as addition, subtraction with fractions, LCM is used for the common denominator. This process simplifies the simplification process.
Find:
We find the smallest number
Given:
What is the smallest number ,which when divided by 7,18,56 and 36, leaves a reminder 0
Step-by-step explanation:
To get to the answer, you need to compute the lowest common multiple (LCM) of the given numbers.
To compute the LCM, we can proceed as follows -
7=1×7
18= 2×3×3
56= 2×2×2×7
36= 2×2×3×3
Basically, I have expanded the numbers as products of prime numbers/factors (and 1 if necessary).
Now, we multiply each prime factor the greatest number of times it occurs in either number's expansion.
So we have,
LCM=2×2×2×3×3×7=504
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