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Last updated on November 29th, 2024

LCM of 4 and 10

Q: How do you derive the LCM of two decimal numbers? Explain using 4.0 and 10.0?

To derive the LCM of two decimal numbers, follow the below steps - First, convert the given decimals to whole numbers. In the given case, 4.0 and 10.0 are already whole. However, if there is a case where the decimal is, say, 4.5, multiply it by 10 to convert them to a whole number, which will be 45. After converting them into whole numbers, ascertain the LCM of the digits using any of the methods, i.e., the listing multiples method, the division method or the prime factorization method. The LCM (4,10)= 20

Q: What is the LCM formula using the HCF?

The LCM can be found using the formula: LCM (a, b)= a×b/HCF(a, b) For 4 and 10, HCF(4,10)= 2 So, LCM(4,10)=4×10/2 = 20

Q: Why is the LCM of 4 and 10 not simply their product (4 × 10 = 40) ?

No, multiplying gives you the product of the numbers, in this case,40. LCM, however, is the smallest common multiple that can be ascertained following the listing multiples method, prime factorization, or the division method.

Professor Greenline Explaining Math Concepts

Foundation

Intermediate

Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 4 and 10. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM helps to solve problems with fractions and scenarios like scheduling or aligning repeating cycle of events.

What is the LCM of 4 and 10?

The LCM of 4 and 10 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations like addition and subtraction with fractions to equate the denominators.

How to find the LCM of 4 and 10?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

LCM of 4 and 10 using the Listing Multiples Method

The LCM of 8 and 10 can be found using the following steps:

Steps:

1. Write down the multiples of each number

Multiples of 4 = 4, 8, 12, 16, 20, 24, …

Multiples of 10 = 10, 20, 30, 40, …

2. Ascertain the smallest multiple from the listed multiples

The smallest common multiple is 20. Thus, LCM(4, 10) = 20.

LCM of 4 and 10 using the Prime Factorization Method

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Steps:

1. Find the prime factors of each number:

Prime factorization of 4 = 2×2

Prime factorization of 10 =2×5

2. Take the highest powers of each prime factor and multiply the highest powers to get the LCM:

LCM(4, 10) = 2×2×5= 20

LCM of 4 and 10 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, and then multiplying the divisors to find the LCM.

Steps:

1. Write the numbers:

2. Divide by common prime factors

3. Multiply the divisors

So, LCM(4, 10) = 20

Common Mistakes and how to avoid them while finding the LCM of 4 and 10

LCM of 4 and 10 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Buses A and B run every 4 days and 10 days respectively. In how many days will they run together again?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Explanation

Problem 2

A company has meetings every 4 days and 10 days. If both the conference rooms are booked today, when will they next be booked together ?

Explanation

Problem 3

Warehouse XYZ restocks sugar every 4 days and pulses every 10 days. If both the goods are restocked today, when will they next be restocked?

Explanation

Problem 4

The sprinkler watering system waters every 4 days and the drip watering system waters every 10 days. On which day do they have to be turned on together?

Explanation

FAQs on LCM of 4 and 10

1.How do you derive the LCM of two decimal numbers? Explain using 4.0 and 10.0?

2.What is the LCM formula using the HCF?

3.Why is the LCM of 4 and 10 not simply their product (4 × 10 = 40) ?

Important glossaries for LCM of 4 and 10

Multiple: A number multiplied with an integer.

Prime Factor: A natural number (other than 1) whose factors that are one and itself.

Prime Factorization: Breaking down a number into its prime factors is called Prime Factorization.

Relatively Prime Numbers: Numbers that have no common factors other than 1.

Fraction: A representation of a part of a whole.

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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.