Question

find the lcm of 60,75,120 by using common
prime factors

Answer 1

The least common multiple or the LCM of the three numbers is 120.

To find the least common multiple (LCM) of 60, 75, and 120 using common prime factors, we can follow these steps:

LCM stands for the Least Common Multiple. It is the smallest positive integer that is divisible by two or more given numbers without leaving a remainder. In other words, the LCM is the smallest common multiple shared by the given numbers.

Step 1: Prime factorize each number:

$60 = 2^2 \times 3 \times 5\\75 = 3 \times 5^2\\120 = 2^3 \times 3 \times 5$

Step 2: Identify the highest power of each prime factor that appears in any of the numbers:

Prime factor 2: highest power = $2^3$

Prime factor 3: highest power = 3

Prime factor 5: highest power = $5^2$

Step 3: Multiply the prime factors with their highest powers to find the LCM:

LCM $= 2^3 \times 3 \times 5^2 = 8 \times 3 \times 25= 600$

Therefore, the LCM of 60, 75, and 120 is 600.

Learn more about least common multiple (LCM)  visit:

https://brainly.in/question/23449119

https://brainly.in/question/7308596

#SPJ1