Question

The LCM of 960 and 240 is :

• A. 960
• B. 240
• C. 60
• D. 15

Hint:

Whenever you are asked to find the LCM of two numbers, always check if the larger number is divisible by the smaller one first.
If it is, the larger number is the LCM, and the smaller number is the HCF.
This simple observation can save you from writing out prime factorizations during the exam!

Answer 1

The Correct Option is A

Step 1: Use the GCD-LCM link instead of prime factors.
For any two positive integers $a$ and $b$, the product of their LCM and their HCF always equals the product of the numbers themselves:
\[ \text{LCM}(a,b) \times \text{HCF}(a,b) = a \times b \]
So if we find the HCF of 960 and 240 first, we can get the LCM in one step without breaking either number into prime factors.

Step 2: Find the HCF by the Euclidean division method.
Divide the larger number by the smaller one and keep repeating with the remainder until the remainder becomes 0.
\[ 960 = 240 \times 4 + 0 \]
The remainder is 0 on the very first division, so the HCF is the divisor at this stage, which is 240.

Step 3: Get the LCM from the HCF.
Using the relation from Step 1:
\[ \text{LCM}(960, 240) = \frac{960 \times 240}{\text{HCF}(960, 240)} = \frac{960 \times 240}{240} \]
The 240 in the numerator and denominator cancel out:
\[ \text{LCM}(960, 240) = 960 \]

Step 4: Final Answer.
The LCM of 960 and 240 is 960, so option (A) is correct. \[ \boxed{960} \]