Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 64 and 84 the smallest integer that is 1344 that is divisible by both numbers.
Least Common Multiple (LCM) of 64 and 84 is 1344.
LCM(64,84) = 1344
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 64 and 84. First we will calculate the prime factors of 64 and 84.
Prime Factorization of 64
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:
64 = 26
Prime Factorization of 84
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:
84 = 22×31×71
Now multiplying the highest exponent prime factors to calculate the LCM of 64 and 84.
LCM(64,84) = 26×31×71
LCM(64,84) = 1344
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1, 2, 4, 8, 16, 32, 64
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 64 and 84, than apply into the LCM equation.
GCF(64,84) = 4
LCM(64,84) = ( 64 × 84) / 4
LCM(64,84) = 5376 / 4
LCM(64,84) = 1344
(i) The LCM of 84 and 64 is associative
LCM of 64 and 84 = LCM of 84 and 64
1. What is the LCM of 64 and 84?
Answer: LCM of 64 and 84 is 1344.
2. What are the Factors of 64?
Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.
3. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
4. How to Find the LCM of 64 and 84?
Answer:
Least Common Multiple of 64 and 84 = 1344
Step 1: Find the prime factorization of 64
64 = 2 x 2 x 2 x 2 x 2 x 2
Step 2: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1344 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 7
Step 4: Therefore, the least common multiple of 64 and 84 is 1344.