Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 61 and 64 the smallest integer that is 3904 that is divisible by both numbers.
Least Common Multiple (LCM) of 61 and 64 is 3904.
LCM(61,64) = 3904
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 61 and 64. First we will calculate the prime factors of 61 and 64.
Prime Factorization of 61
61 | 61 |
1 |
Prime factors of 61 are 61. Prime factorization of 61 in exponential form is:
61 = 611
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
Now multiplying the highest exponent prime factors to calculate the LCM of 61 and 64.
LCM(61,64) = 26×611
LCM(61,64) = 3904
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1, 61
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1, 2, 4, 8, 16, 32, 64
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 61 and 64, than apply into the LCM equation.
GCF(61,64) = 1
LCM(61,64) = ( 61 × 64) / 1
LCM(61,64) = 3904 / 1
LCM(61,64) = 3904
(i) The LCM of 64 and 61 is associative
LCM of 61 and 64 = LCM of 64 and 61
1. What is the LCM of 61 and 64?
Answer: LCM of 61 and 64 is 3904.
2. What are the Factors of 61?
Answer: Factors of 61 are 1, 61. There are 2 integers that are factors of 61. The greatest factor of 61 is 61.
3. 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.
4. How to Find the LCM of 61 and 64?
Answer:
Least Common Multiple of 61 and 64 = 3904
Step 1: Find the prime factorization of 61
61 = 61
Step 2: Find the prime factorization of 64
64 = 2 x 2 x 2 x 2 x 2 x 2
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 3904 = 2 x 2 x 2 x 2 x 2 x 2 x 61
Step 4: Therefore, the least common multiple of 61 and 64 is 3904.