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Last updated on November 29th, 2024

LCM of 30 and 75

Q: What is the GCF of 30 and 75?

— 30 factors — 1,2,3,5,6,10,15,30 — 75 factors — 1,3,5,15,25,75 HCF(30,75) = 15

Q: Find the LCM of 25 and 75.

— Multiples of 25 = 25,50,75,… — Multiples of 75 = 75,… LCM(25,75) = 75

Q: What is the LCM of 40 and 75?

— 40 = 2×2×2×5 — 75 = 3×5×5 LCM (40,75) = 600

Q: What is the LCM of 50 and 75?

— 50 = 2×5×5 — 75 = 3×5×5 LCM(50,75) = 150

Q: What is the LCM of 30,45 and 75?

— 30 = 2×3×5 — 45 = 3×3×5 — 75 = 3×5×5 LCM (30,45,75) = 450

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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.

What is LCM 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.

LCM of 30 and 75 using listing multiples method

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

LCM of 30 and 75 using prime factorization method

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

LCM of 30 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 (30,75) = 150

Common mistakes and how to avoid them in LCM of 30 and 75

LCM of 30 and 75 Examples

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Problem 1

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.

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Explanation

Problem 2

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.

Explanation

Problem 3

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?

Explanation

FAQs on the LCM of 30 and 75

1.What is the GCF of 30 and 75?

2.Find the LCM of 25 and 75.

3. What is the LCM of 40 and 75?

4.What is the LCM of 50 and 75?

5.What is the LCM of 30,45 and 75?

Important glossaries for LCM of 30 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, 30 is written as the product of 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.