The L.C.M. of two numbers is 210 and their H.C.F. is 3. If the first number is divided by 3, the quotient is 7 and the remainder is 0. The second number is:
30
Given that the first number divided by 3 gives quotient 7 with remainder 0, the first number is \(3\times 7 = 21\).
For any two numbers, product = LCM × HCF, i.e. \(a\times b = \text{LCM}\times\text{HCF}\).
Substitute: \(21\times b = 210\times 3 = 630\).
Solve: \(b = \dfrac{630}{21} = 30\).
Hence, the second number is 30.
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Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
