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
- Find the smallest number which when divided by 8, 9, and 12 leaves a remainder of 5 in each case.
- What is the least square number that is divisible by 8, 12, and 20?
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?
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
