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Last updated on November 30th, 2024

LCM of 10 and 12

Q: How do you find the LCM of 10 and 12 using a Venn diagram?

Follow the below steps to ascertain the LCM of 10 and 12 using a Venn diagram; 1. List the prime factors of the digits — Prime factorization of 10 = 2 × 5 — Prime factorization of 12 = 2 × 2 × 3 2. Place the factors in the diagram 2 is a common factor, place it in the overlapping section. 5,2,3 are unique factors ascertained after the common factor for 10 and 12. Place them in their own section. Now, multiply both the common and the unique factors — 2 × 2 × 3×5 = 60 The LCM (10,12) = 60.

Q: What is the LCM formula using the HCF? Explain for the numbers 10 and 12.

The LCM can be found using the formula, and as explained with the example given below. LCM (a, b)= a×b/HCF(a, b) For 6 and 10, HCF(10,12)= 2 So, LCM(10,12)=10×12/2 = 60

Q: How do you derive the LCM of two decimal numbers? Explain using 10.0 and 12.0.

To derive the LCM of two decimal numbers, follow the below steps; First, convert the given decimals to whole numbers. In the given case, 10.0 and 12.0 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 (10,12)= 60

Q: How do you find the LCM of algebraic expressions?

For algebraic expressions, find the LCM by factoring each expression and then choosing the highest power of each variable. For example, Find the LCM of x2y and xy3 Factor each term as follows x2y = x2 × y —---> highest power = x2 xy3 = x × y3 —---> highest power = y3 Multiply the highest powers —---> x2y3 LCM(x2y, xy3) = x2y3

Professor Greenline Explaining Math Concepts

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Advance Topics

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 10 and 12. 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 10 and 12?

The LCM of 10 and 12 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.

How to find the LCM of 10 and 12?

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

LCM of 10 and 12 using the Listing Multiples Method

The LCM of 10 and 12 can be found using the following steps:

Steps:

1. Write down the multiples of each number

— Multiples of 10 = 10, 20, 30, 40, 50, 60, …

— Multiples of 12 = 12, 24, 36, 48, 60, …

2. Ascertain the smallest multiple from the listed multiples

— The smallest common multiple is 60.

Thus, LCM(10, 12) = 60.

LCM of 10 and 12 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 the numbers:

— Prime factorization of 10 = 2 × 5

— Prime factorization of 12 = 2 × 2 × 3

2. Take the highest powers of each prime factor:

— Highest power of 2 = 2²

— Highest power of 3 = 3

— Highest power of 5 = 5

Multiply the highest powers to get the LCM:

LCM(10, 12) = 2² × 3 × 5 = 60

LCM of 10 and 12 using the Division Method

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

Steps:

1. Write the numbers:

2. Divide by common prime factors and multiply the divisors:

— 2 × 2 × 3 × 5 = 60

Thus, LCM(10, 12) = 60.

Common Mistakes and how to avoid them while finding the LCM of 10 and 12

LCM of 10 and 12 Examples

Ray, the Character from BrightChamps Explaining Math Concepts

Problem 1

Bus A and bus B, run every 10 and 12 days, both leave the station today. When will they next leave the station on the same day again?

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

Explanation

Problem 2

In a neighborhood park, the fountain show is turned on every 10 minutes, and the light show every 12 minutes. If both the shows are turned on at the same time, when will they next be turned on together again?

Explanation

Problem 3

The sprinkler watering system waters every 10 days and the drip watering system waters every 12 days. On which day do they have to be turned on together?

Explanation

Problem 4

A car mechanic services a red car every 10 days and a blue car every 12 days. If the cars are serviced today, when will they be serviced next together?

Explanation

FAQs on LCM of 10 and 12

1.How do you find the LCM of 10 and 12 using a Venn diagram?

2.What is the LCM formula using the HCF? Explain for the numbers 10 and 12.

3.How do you derive the LCM of two decimal numbers? Explain using 10.0 and 12.0.

4.How do you find the LCM of algebraic expressions?

Important glossaries for LCM of 10 and 12

Multiple: A number and any integer multiplied.

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

Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization.

Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.

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.