SME
Grade 6 Math · Problem type
Prime factorization
Use this for “Find the greatest common factor of 84 and 60.”
Diagram
40 = 2³ × 5.
56 = 2³ × 7.
Shared primes (ringed): 2 × 2 × 2 = 8.
This is an example. Type your own values to start a new problem.
The
greatest
common
factor
of
a
and
b
is
g
Least common multiple
worked out (not typed)
Formulas
shared prime factors of 40 and 56: 8
Primes both numbers share, multiplied = greatest common factor
8 × (40 ÷ 8) × (56 ÷ 8) = 280
GCF × primes left in the first × primes left in the second = least common multiple
Assumptions
•
Split each number until every branch ends in a prime.
•
The primes both numbers share multiply to the GCF.
•
The LCM is the GCF times the primes left over from each number.
Step-by-step
WE KNOW
First number: 40
Second number: 56
FIND
greatest common factor, least common multiple
Step 1 · Find greatest common factor
shared prime factors of 40 and 56: ?
Primes both numbers share, multiplied = greatest common factor
Write each number as primes. Multiply the primes they share, as many times as both have them.
40
=
2
×
2
×
2
×
5
=
2
3
×
5
56
=
2
×
2
×
2
×
7
=
2
3
×
7
Shared primes: 2 × 2 × 2 = 8
Greatest common factor = 8
Step 2 · Find least common multiple
8 × (40 ÷ 8) × (56 ÷ 8) = ?
GCF × primes left in the first × primes left in the second = least common multiple
Start with the shared primes (the GCF). Multiply by the primes left over from each number.
Left over: 40 ÷ 8 = 5 and 56 ÷ 8 = 7
8 × 5 × 7 = 280
Least common multiple = 280
Check
Put the numbers back in. Both sides should match.
shared prime factors of 40 and 56: 8 ✓
8 × 280 = 40 × 56 ✓
Topic check
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Related lessons
Greatest common factor and least common multiple
Main lesson
Least common multiple
Use this for “What is the least common multiple of 6 and 9?”
Factor expressions using the GCF
Use this for “Write 36 + 8 as a product of the GCF and a sum.”
GCF or LCM?
Use this for “Does the problem need the GCF or the LCM?”