If the sum of LCM and HCF of two numbers is 50 and their LCM is 20 more than their HCF. Then the product of the two numbers will be: - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

A
525
B
425
C
625
D
325

Solution:

Concept- LCM: least common multiple of two integers is called LCM.
HCF: The highest common factor of two integers is called HCF.
Given, the sum of LCM and HCF of two numbers is 50,

x + y = 50 \dots \dots . (1)

Their LCM exceeds their HCF by 20.

x = y + 20 \dots \dots \dots . . (2)

Put the value of x in equation (1),

y + 20 + y = 50

2 y + 20 = 50

2 y = 50 - 20

y = \frac{30}{2}

y = 15

Add y's value to the equation (2),

x = y + 20

x = 15 + 20

x = 35

LCM= 35
HCF= 15
Product of two numbers,

15 \times 35 = 525

Hence, the correct option is 1.

Solution:

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