m and n are two 2-digit numbers, out of which one is even and the other is odd. If \(mn = 180\), then what is the least common multiple of m and n?
60
Since \(mn = 180\) and both m and n are 2-digit numbers with one even and one odd, the two-digit factor pairs of 180 need to be checked.
The pair \(15 \times 12 = 180\) has both factors as 2-digit numbers, with 15 odd and 12 even, satisfying the condition.
Writing \(15 = 3 \times 5\) and \(12 = 2^2 \times 3\), the LCM is \(2^2 \times 3 \times 5 = 60\).
Hence, the least common multiple of m and n is \(60\).
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?
The sum of two numbers is 1215 and their HCF is 81. How many such pairs of numbers can be formed?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
