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To determine the Least common Multiple:
Find the prime factorization for each number using exponents.
For each prime factor, write the base with the greatest exponent.
Multiply.
Finding the LCM Using Prime Factorization
Find the LCM of 36 and 24
36
24
/\
/\
2 18
2 12
/\
/\
2 9
2 6
/\
/\
3 3
2 3
36= 2×2×3×3
24= 2×2×2×3
22 x 32
23 x 3
23 x 3 2
The LCM of 36 and 24 is 2X2X2X3X3 = 72
FINDING THE LCM USING PRIME FACTORIZATION
1. Prime factor each number. Write using exponents.
2. For each prime factor, write the base with the greatest
exponent.
3. Multiply all together.
Find the GCF of 36 and 24
36
24
/\
/\
2 18
2 12
/\
/\
2 9
2 6
/\
/\
3 3
2 3
36= 2×2×3×3
24= 2×2×2×3
22 x 3 2
23 x 3
22 x 3
The GCF of 36 and 24 is 2×2×3=12
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