GCF, LCM, and Factoring Sums
Aligned to 6.NS.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
The GCF (greatest common factor) is the largest number that divides both numbers evenly; the LCM (least common multiple) is the smallest number both divide into. You can also pull the GCF out of a sum using the distributive property.
Worked examples
Example 1
For 36 and 8: the GCF is 4. So 36 + 8 = 4 × 9 + 4 × 2 = 4 × (9 + 2). The LCM of 4 and 6 is 12, the first multiple they share.
Example 2
For 45 and 30: the GCF is 15, so 45 + 30 = 15 × (3 + 2) = 15 × 5.
Example 3
LCM tells you when cycles line up. A bus every 12 minutes and one every 18 minutes arrive together every 36 minutes.
Practice questions
- Find the GCF of 24 and 60.
- Find the LCM of 8 and 12.
- Rewrite 45 + 30 as the GCF times a sum, using the distributive property.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
MCD, mcm y Factorizar Sumas
El MCD (máximo común divisor) es el número más grande que divide exactamente a ambos números; el mcm (mínimo común múltiplo) es el número más pequeño que ambos dividen. También puedes sacar el MCD de una suma usando la propiedad distributiva.
Ejemplo 1: Para 36 y 8: el MCD es 4. Entonces 36 + 8 = 4 × 9 + 4 × 2 = 4 × (9 + 2). El mcm de 4 y 6 es 12, el primer múltiplo que comparten.
Ejemplo 2: Para 45 y 30: el MCD es 15, así que 45 + 30 = 15 × (3 + 2) = 15 × 5.
Ejemplo 3: El mcm te dice cuándo coinciden los ciclos. Un autobús cada 12 minutos y otro cada 18 llegan juntos cada 36 minutos.
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