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?
Important Questions from LCM and HCF
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
