Last updated on May 26th, 2025
The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 30 and 75. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronise traffic lights and when making music. In this article, let’s now learn to find LCMs of 30 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.
Step1: List the multiples of each of the numbers;
30 = 30,60,90,120,150,180,…
75= 75,150,225,300,…
Step 2: Find the smallest number in both the lists
LCM (30,75) = 150
Step 1: Prime factorize the numbers
30 = 2×3×5
75 = 3×5×5
Step 2:find highest powers.
Step 3:Multiply the highest powers of the numbers
LCM(30,75) = 150
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!
Prove that the LCM of two numbers a and b, where GCF(a, b)=d, can be written as LCM(a, b)=a×b LCM(a, b)=a×b​ using a=30 and b=75.
a = 30, b=75
d=GCF(30,75)=15
By the formula: LCM(30,75)= 30×75/GCF(30,75)
30×75/15=150
The LCM matches the direct calculation using prime factorization.
This problem uses the property that the product of two numbers divided by their GCF gives the LCM, providing a mathematical verification.
If the GCF of two numbers is 15 and one of the numbers is 30, use the formula to find the LCM of these two numbers.
Formula: LCM(a, b)=a×b/GCF(a, b)
Given a=30, GCF(a, b)=15 and let b=75
LCM(30,75)=30×75/15=2250/15=150
Using the relationship between the GCF and LCM, we can quickly compute the LCM of the two numbers.
John exercises every 30 days and Sarah exercises every 75 days. If they both exercised today, in how many days will they exercise together again?
The number of days when they will both exercise together again is the LCM of 30 and 75.
LCM(30,75)=150
So, they will both exercise together again in 150 days.
The LCM of their exercise intervals gives the earliest day they will coincide again.
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.