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Last updated on November 29th, 2024

LCM of 60 and 75

Q: Find the GCF of 60 and 75 and list all the factors of the numbers.

Factors of; 60–1,2,3,4,5,6,10,12,15,20,30,60 75–1,3,5,15,25,75 GCF(60,75) = 15

Q: Find the LCM of 60,75 and 90.

Prime factorization of the numbers 60,75 and 90; 60 = 2×2×3×5 75 = 3×5×5 90= 3×3×2×5 LCM (60,75,90) = 900

Q: Find the LCM of 30,60 and 75?

Prime factorization of the numbers 30,60 and75; 30 =2×3×5 60 = 2×2×3×5 75 = 3×5×5 LCM (30,60,75) = 300

Q: Find the LCM of 50,60 and 75?

Prime factorization of the numbers; 50 = 2×5×5 60 = 2×2×3×5 75 = 3×5×5 LCM (50,30,60) = 300

Q: Find the LCM of 60,75 and 105?

Write down the multiples of the numbers 60 = 60,120,180,240,30,…2100 75 = 75,150,225,300,….2100 105 = 105,210,315,420,…2100 LCM (60,75,105) = 2100

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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

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Problem 1

Verify that the relationship between GCD and LCM holds true for 60 and 75: LCM(a, b)×GCD(a, b)=a×b

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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.