Question
Download Solution PDFThe LCM of two numbers is 12 times their HCF, and the difference between their LCM and HCF is 4829. When one of these two numbers is divided by 375, the quotient is 3 and the remainder is 192. The other number is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
LCM = 12 × HCF
LCM - HCF = 4829
One number divided by 375 gives quotient 3 and remainder 192.
Formula used:
LCM × HCF = Product of two numbers
Dividend = Divisor × Quotient + Remainder
Calculation:
Let HCF = h, then LCM = 12h.
According to question,
12h - h = 4829
11h = 4829 = 4829 / 11
h = 439
HCF = 439, LCM = 12 × 439 = 5268.
Now, the first number:
Number = Divisor × Quotient + Remainder
Number = 375 × 3 + 192
Number = 1125 + 192
Number = 1317
Let the other number be 'x'.
LCM × HCF = Product of two numbers:
5268 × 439 = 1317 × x
2312652 = 1317x
x = 2312652 / 1317
x = 1756
∴ The other number is 1756.
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