Euclidean Algorithm of 48 and 18

The GCF of 48 and 18 is 6.

Quick math

  • 48 = 2 × 18 + 12
  • 18 = 1 × 12 + 6
  • 12 = 2 × 6 + 0
  • The last non-zero remainder is 6.
GCF
6
Division steps
3
LCM
144
Coprime
No
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Euclidean Algorithm for 48 and 18

The GCF of 48 and 18 is 6. The Euclidean algorithm finds it in 3 steps of division with remainder.

Handwritten notebook page running the Euclidean algorithm on 48 and 18
The Euclidean algorithm on 48 and 18 worked out by hand: the GCF is 6.

The Division Steps

  1. 48 = 2 × 18 + 12
  2. 18 = 1 × 12 + 6
  3. 12 = 2 × 6 + 0

Reading the Result

The last non-zero remainder is 6, so the GCF of 48 and 18 is 6. Both 48 and 18 divide evenly by 6.

The LCM of 48 and 18

LCM = 48 × 18 ÷ 6 = 144. Try other pairs in the Euclidean Algorithm Calculator.

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Euclidean Algorithm of 48 and 18: FAQs

What is the GCF of 48 and 18 by the Euclidean algorithm?

The GCF of 48 and 18 is 6. The steps are: 48 = 2 × 18 + 12; 18 = 1 × 12 + 6; 12 = 2 × 6 + 0. The last non-zero remainder is 6.

How does the Euclidean algorithm work?

Divide the larger number by the smaller one and keep the remainder. Then divide the smaller number by that remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF.

How many steps does it take for 48 and 18?

It takes 3 division steps to reach a remainder of 0.

What is the LCM of 48 and 18?

The LCM of 48 and 18 is 144, found by dividing 48 × 18 by the GCF 6.

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