To find the LCM (Least Common Multiple) of two numbers when their product and HCF (Highest Common Factor) are given, we can use the relationship between the product of two numbers, their HCF, and their LCM. The formula is:
\(\text{Product of the two numbers} = \text{HCF} \times \text{LCM}\)
In this problem, the product of the two numbers is given as 2025, and their HCF is 15. We are required to find their LCM. Substitute the given values in the formula:
\(2025 = 15 \times \text{LCM}\)
Solve for LCM:
\(\text{LCM} = \frac{2025}{15}\)
Now, perform the division:
\(\text{LCM} = 135\)
Thus, the LCM of the two numbers is 135.
Let's verify that 135 is the correct answer. The options given are:
- 135
- 225
- 105
- 1350
The correct answer is 135. The calculation confirms the reasoning based on the relationship between the product, HCF, and LCM of two numbers. Therefore, 135 is the correct LCM.
Similar Questions
The product of two 2-digit numbers is 2160 and their H.C.F. is 12. The numbers are
The LCM of 2³ x 9² x 13, 2² x 13² x 19 and 9³ x 13² x 19² is:
A and B start running at the same time and from the same point around a circle. If A can complete one round in 40 seconds and B in 50 seconds, how many seconds will they take to reach the starting point simultaneously?
The least number, which when divided by 5, 6, 7, and 8 leaves a remainder 3 in each case, but when divided by 9 leaves no remainder, is:
Arvind and Chetan started running simultaneously from the same point in the same direction on a circular track of length 210 m. If Arvind takes 180 seconds to complete one round, and Chetan takes 420 seconds to complete one round, after how much time will they meet for the first time at the starting point on the track?
Find the LCM of 12, 18, 30.
- What is the least square number that is divisible by 8, 12, and 20?
- Find the smallest number which when divided by 8, 9, and 12 leaves a remainder of 5 in each case.
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?
