Study Guide · Maths

How to Find the LCM of 510 and 92?

Finding the massive Lowest Common Multiple (LCM) of 510 and 92 is a highly famous, massively repeated standard board exam question from the Class 10 Mathematics chapter 'Real Numbers'. Because the numbers are large, we must strictly use the massive Prime Factorization method.

Question (Click to Flip)

Let's heavily verify the massive formula.

Answer

Left Side (LCM × HCF): $23460 \times 2 = $ 46920.
Right Side (Product of numbers): $510 \times 92 = $ 46920.
Both sides match perfectly, proving the massive answer is 100% physically correct.

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Key Facts

In massive Class 10 board exams, you are physically forced to violently verify your answer using the golden mathematical formula: LCM × HCF = Product of the two numbers.

Step 1: Prime Factorization of the Heavy Numbers

Let's break down massive 510: $510 = 2 \times 255$ $= 2 \times 3 \times 85$ $= 2 \times 3 \times 5 \times 17$
Let's break down heavy 92: $92 = 2 \times 46$ $= 2 \times 2 \times 23$ $= 2^2 \times 23$

Step 2: Calculating the Massive LCM

The strict mathematical rule for LCM is to physically write down every single prime number that appeared, and aggressively take its highest power.

Prime numbers involved: 2, 3, 5, 17, and 23.
The highest power of 2 is $2^2$.
The highest power of the others is just 1.
LCM = $2^2 \times 3 \times 5 \times 17 \times 23$
LCM = $4 \times 3 \times 5 \times 17 \times 23$ = 23460.

Step 3: Calculating the Massive HCF

For HCF (Highest Common Factor), we strictly take ONLY the prime numbers that are heavily common in both lists, with the absolute lowest power.

Only the number '2' is massively common in both.
The absolute lowest power is $2^1$.
Therefore, the HCF is 2.

Questions and Answers

Let's heavily verify the massive formula.+

- Left Side (LCM × HCF): $23460 \times 2 = $ **46920**. - Right Side (Product of numbers): $510 \times 92 = $ **46920**. - Both sides match perfectly, proving the massive answer is 100% physically correct.

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