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Greatest common factor & least common multiple

Factors & multiples

Japanese school year: Elementary 5

What you learn

You will learn methods to determine the greatest common factor and least common multiple of two or more numbers. These concepts are essential for simplifying fractions, finding common denominators, and solving scheduling problems. A solid grasp of listing individual factors and multiples is recommended.

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Key points

The largest common factor among numbers is called the greatest common divisor (GCD). It is used to simplify fractions into their simplest form.

The smallest shared positive multiple of numbers is called the least common multiple (LCM). It is used to find a common denominator when adding or subtracting fractions.

This is ladder division (short division), dividing two numbers simultaneously by common factors. Multiplying common divisors gives the GCD, while multiplying all divisors and final quotients gives the LCM.

This formula shows that the product of two positive integers aa and bb equals the product of their GCD and LCM. It is useful for finding one value when the other is already known.

a×b=gcd⁡(a,b)×lcm⁡(a,b)a \times b = \gcd(a, b) \times \operatorname{lcm}(a, b)

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