Study Guide · Maths

What is the LCM of 12 and 18?

Calculating the Lowest Common Multiple (LCM) of two specific numbers is a highly massive, essential skill for middle school mathematics. Let's mathematically find the absolute exact LCM for the heavy numbers 12 and 18 using two different massive methods.

Question (Click to Flip)

Can I use the massive formula (a × b) / HCF?

Answer

Yes! The massive math formula states: $LCM = (Number 1 \times Number 2) / HCF$. So, $(12 \times 18) / 6 = 216 / 6 = $ 36.

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Key Facts

The heavy HCF (Highest Common Factor) of 12 and 18 is exactly 6, because 6 is the absolute largest number that can mathematically divide both 12 and 18 perfectly without leaving a massive remainder.

Method 1: The 'Listing Multiples' Method

This is the absolute simplest massive method. We physically write down the heavy multiplication tables for both numbers until we violently find the first matching number.

Massive Multiples of 12: 12, 24, 36, 48, 60, 72...
Massive Multiples of 18: 18, 36, 54, 72...
As you can physically see, the number 36 is the absolute first (lowest) number that appears in both heavy lists. Therefore, the LCM is 36.

Method 2: The 'Prime Factorization' Method

This massive method is heavily used in higher classes for larger numbers.

Step 1: Break massive 12 into prime numbers: $12 = 2 \times 2 \times 3$ (or $2^2 \times 3^1$).
Step 2: Break massive 18 into prime numbers: $18 = 2 \times 3 \times 3$ (or $2^1 \times 3^2$).
Step 3: Build the LCM: To mathematically violently construct the LCM, take the absolute highest massive power of every prime number you see.
Highest power of 2 is $2^2$ (4). Highest power of 3 is $3^2$ (9).
LCM = $4 \times 9$ = 36.

Questions and Answers

Can I use the massive formula (a × b) / HCF?+

Yes! The massive math formula states: $LCM = (Number 1 \times Number 2) / HCF$. So, $(12 \times 18) / 6 = 216 / 6 = $ **36**.

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