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151 LearnersLast updated on November 29th, 2024
LCM of 60 and 75
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.
What is LCM 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.
LCM of 60 and 75 using listing multiples method
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
LCM of 60 and 75 using prime factorization method
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
LCM of 60 and 75 using division method
- Write the numbers in a row
- Divide them with a common prime factor
- Carry forward numbers that are left undivided
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM
- LCM (60,75) = 300
Common mistakes and how to avoid them while finding the LCM of 60 and 75
LCM of 60 and 75 Examples
Problem 1
Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b
Explanation
Problem 2
What percentage of the product of 60 and 75 is their LCM?
Explanation
Problem 3
If the LCM of 60 and a missing number xxx is 300, what is xxx?
Explanation
Problem 4
Is 600 a common multiple of 60 and 75?
Explanation
FAQs on the LCM of 60 and 75
1. Find the GCF of 60 and 75 and list all the factors of the numbers.
2.Find the LCM of 60,75 and 90.
3.Find the LCM of 30,60 and 75?
4.Find the LCM of 50,60 and 75?
5. Find the LCM of 60,75 and 105?
Important glossaries for LCM of 60 and 75
- Multiple: the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75.
- Prime Factor: A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind.
- Prime Factorization: breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5.
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
