LCM of 510 and 92

LCM of 510 and 92 is 23460. LCM stands for Lowest Common Multiple or Least Common Multiple. LCM of two integers, 510 and 92, is the smallest positive integer 23460 which is divisible by both 510 and 92 with no remainder.

In this article, we will learn about what is the LCM of 510 and 92, and how to find LCM of 510 and 92 using various methods like Prime factorization, Listing Multiples, and By Long Division Method.

What is LCM of 510 and 92?

LCM of 510 and 92 is 23460

This means that 23460 is the smallest common integer which is divisible by both 92 and 510 without leaving any remainder.

LCM of 510 and 92 Calculator

LCM of 510 and 92 can be calculated using the following calculator:

How to Find LCM of 510 and 92

The various methods used to find LCM of 510 and 92 numbers are as follows:

• LCM of 510 and 92 by Prime Factorization
• LCM of 510 and 92 by Listing Multiples
• LCM of 510 and 92 by Long Division

LCM of 510 and 92 by Prime Factorization

Below are the steps for finding LCM of 510 and 92 by prime factorization method:

• Find the prime factors of the given numbers by repeated division method.
• Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.
• The product of these factors with the highest powers is the LCM of the given numbers.

Prime factorization of 510 and 92, respectively, is given by:

• 510 = 2 × 3 × 5 × 17
• 92 = 2 × 2 × 23 = 2² × 23

LCM (510, 92) = 2² × 3 × 5 × 17 × 23 = 23460

LCM of 510 and 92 by Listing Multiples

Below are the steps for finding LCM of 510 and 92 by listing multiples:

• List the first few multiples of 510 and 92.
• Mark the common multiples from the multiples of both numbers.
• Select the smallest common multiple. That lowest common multiple is the LCM of the two numbers.

To calculate the LCM of 510 and 92 by listing out the common multiples, list the multiples as:

• Multiples of 510 = 510, 1020, 1530, 2040, 2550, 3060,…, 23460
• Multiples of 92 = 92, 184, 276, 368, 460, 552, 644,…, 23460

Here, 23460 is the first common multiple of both 510 and 92

Therefore, LCM (510, 92) = 23460

LCM of 510 and 92 by Long Division

Below are the steps for finding LCM of 510 and 92 by long division method:

• Divide the numbers, by the smallest prime number.
• If any number is not divisible, then write down that number and proceed further
• Keep on dividing the row of numbers by prime numbers, unless we get the results as 1 in the complete row.
• Now LCM of the numbers will be equal to the product of all the prime numbers we obtained in the division method.

To calculate the LCM of 510 and 92 by the division method, we will divide the numbers by their prime factors as shown:

LCM of 510 and 92 = 2 × 2 × 3 × 5 × 17 × 23 = 23460

LCM and HCF of 510 and 92

Highest Common Factor of 510 and 92 is 2 and the Least Common Multiple of 510 and 92 is 23460.

Also, LCM × HCF = Product of two numbers

• 510 = 2 × 3 × 5 × 17
• 92 = 2 × 2 × 23

LCM (510, 92) = 2² × 3 × 5 × 17 × 23 = 23460

HCF (510, 92) = 2

LCM × HCF = 23460 × 2 = 46920

Product of 510 and 92 = 510 × 92 = 46920

Solved Example on LCM of 510 and 92

Example 1. Find the LCM and HCF of 510 and 92.

Solution:

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23

LCM (510, 92) = 2² × 3 × 5 × 17 × 23 = 23460

HCF (510, 92) = 2

Example 2. The GCD and LCM of two numbers are 2 and 23460 respectively. If one number is 510, find the other number.

Solution:

GCD × LCM = 510 × x (Assume other number to be x)

x = (GCD × LCM)/510

x = (2 × 23460)/510

x = 92

Therefore, the other number is 92.

Example 3. Verify the relationship between GCF and LCM of 510 and 92.

Solution:

LCM(510, 92) × GCF(510, 92) = Product of 510, 92

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23

LCM (510, 92) = 2² × 3 × 5 × 17 × 23 = 23460

HCF (510, 92) = 2

LCM(510, 92) × GCF(510, 92) = 23460 × 2 = 46920 and also,

Product of 510, 92 = 510 × 92 = 46920

Practice Problems on LCM of 510 and 92

Q1. The GCD and LCM of two numbers are 54 and 98 respectively. If one number is 22, find the other number.

Q2. Find the LCM and HCF of 44 and 98.

Q3. Find the LCM if the product of two numbers is 1042 and the GCD is 48.

Q4. Find the LCM of 95 and 150.

FAQs on LCM of 510 and 92

What is the LCM of 510 and 92?

The LCM of 510 and 92 is 23460.

How to Find the LCM of 510 and 92 by Prime Factorization?

510 = 2 × 3 × 5 × 17

92 = 2 × 2 × 23

LCM (510, 92) = 2² × 3 × 5 × 17 × 23 = 23460

What is the LCM and HCF of 510 and 92?

The Highest Common Factor of 510 and 92 is 2 and the Least Common Multiple of 510 and 92 is 23460.

List the methods used to find the LCM of 510 and 92.

The methods used to find the LCM of 510 and 92 are:

• Prime Factorization Method
• Division Method
• Listing multiples.