5. The LCM and the HCF of two positive numbers is 1000 and 50 respectively. Which of the following could
be the pair of such numbers?
(a) 200 and 500
(b) 150 and 250
(C) 50 and 100 (d) 200 and 250
Answers
the answer is 200 and 250
Concept: Highest Common Factor is the full name for HCF in mathematics.
According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or GCD.
Least Common Multiple is the full name for LCM in mathematics.
The least common multiple, or LCM, of two numbers, such as a and b, is written as LCM in mathematics (a,b). The smallest or least positive integer that is divisible by both a and b is known as the LCM.
Given: The LCM and the HCF of two positive numbers is 1000 and 50 respectively
To find: the pair of numbers whose HCF is 50 and LCM is 1000.
Solution: As we know that the product of two numbers is equal to the product of its HCF and LCM.
HCF × LCM = product of two numbers
1000 × 50 = product of two numbers
50000 = product of two numbers
Now, if we look at the first option (a), then product of 200 and 500 is equal to 200 × 500 = 100000 which is not equal to the product of the HCF and the LCM.
For the second option (b), the product of 150 and 250 is 150 × 250 = 37500 which is not equal to the product of the HCF and the LCM.
For the third option (c), 50 and 100 the product of 50 × 100 = 5000 which is not equal to the product of the HCF and the LCM.
For the last option (d), 200 and 250 the product of 200 × 250 = 50000 is equal to the product of the HCF and the LCM.
Hence, the pair of numbers whose HCF is 50 and LCM is 1000 is 200 and 250.
Therefore. option (d) is correct.
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