Free GCD and LCM Calculator

Free Online Math Calculators

Quickly determine:

• Greatest Common Divisor - GCD, aka
  Greatest Common Denominator - GCD, aka
  Greatest Common Factor - GCF, or finally
  Highest Common Factor - HCF and
• Least Common Multiple - LCM, aka
  Lowest Common Multiple - LCM, or
  Smallest Common Multiple - SCM
  Lowest Common Denominator - LCD

between two or three numbers.

You shouldn't mix up those two. If you need a little reminding, scroll below this free calculator to refresh your memory.

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Little intro:

2	×	3	=	6
factor	×	factor	=	multiple (product)

And now the examples of both.

LCD/LCM story: (LCD is not a computer monitor here) ;-)

"Least common denominator of 2 or more whole numbers (integers) is the smallest positive whole number that is a multiple of those numbers."

Here's one application of LCD/LCM. When you're adding or subtracting fractions you must make your denominators the same.

2	+	1	=	2×2	+	1×3	=	4	+	3	=	4 + 3	=	7
3		2		3×2		2×3		6		6		6		6

=> that's when you do go for LCD/LCM, and in this case your LCD = 6

GCF/GCD story:

"Greatest common factor of 2 or more non-zero whole numbers (integers), is the biggest positive number that divides those numbers without a remainder."

And when you're trying to put something in front of parentheses, say:

6a + 3b = 3×(2a + b)

=> that's when you do go for GCF (Greatest Common Factor), and in this case your GCF = 3

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