Last updated on May 26th, 2025
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 60 and 75. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 60 and 75.
We can find the LCM using listing multiples method, prime factorization method and the long division method. These methods are explained here, apply a method that fits your understanding well.
Step 1: List the multiples of each of the numbers;
60 = 60,120,180,240,300,…
75= 75,150,225,300,…
Step 2: Find the smallest number in both the lists
LCM (60,75) = 300
Step 1:Prime factorize the numbers
60 = 2×2×3×5
75 = 3×5×5
Step 2:find highest powers
22,3 and 52
Step 3: Multiply the highest powers of the numbers
22×3×52 = 300
LCM(60,75) = 300
Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid!
Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b
GCD(60, 75) = 15
LCM(60, 75) = 300
LCM (60,75)×GCD(60,75) = 300×15 = 4500
60×75 = 4500
The formula holds because the product of the LCM and GCD equals the product of the original numbers.
What percentage of the product of 60 and 75 is their LCM?
Product of 60 and 75 = 60 × 75 = 4500
LCM = 300
Percentage = 300/4500×100 = 6.67%
The LCM is 6.67% of the product of the two numbers.
If the LCM of 60 and a missing number xxx is 300, what is xxx?
LCM(60,x) = 300
Prime factorization of 60 = 2² × 3 × 5
Since 300 = 2² × 3 × 5²,
the missing number x must provide the extra factor of 5.
Thus, x=75
The missing number x is the number that would provide the required factors to make the LCM 300.
Is 600 a common multiple of 60 and 75?
600/60 = 10
600/75 = 8
Since 600 is divisible by both 60 and 75, it is a common multiple. However, it is not the least common multiple, as the LCM is 300.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.