Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 63 and 65 the smallest integer that is 4095 that is divisible by both numbers.
Least Common Multiple (LCM) of 63 and 65 is 4095.
LCM(63,65) = 4095
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 63 and 65. First we will calculate the prime factors of 63 and 65.
Prime Factorization of 63
3 | 63 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:
63 = 32×71
Prime Factorization of 65
5 | 65 |
13 | 13 |
1 |
Prime factors of 65 are 5,13. Prime factorization of 65 in exponential form is:
65 = 51×131
Now multiplying the highest exponent prime factors to calculate the LCM of 63 and 65.
LCM(63,65) = 32×51×71×131
LCM(63,65) = 4095
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1, 3, 7, 9, 21, 63
Factors of 65
List of positive integer factors of 65 that divides 65 without a remainder.
1, 5, 13, 65
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 63 and 65, than apply into the LCM equation.
GCF(63,65) = 1
LCM(63,65) = ( 63 × 65) / 1
LCM(63,65) = 4095 / 1
LCM(63,65) = 4095
(i) The LCM of 65 and 63 is associative
LCM of 63 and 65 = LCM of 65 and 63
1. What is the LCM of 63 and 65?
Answer: LCM of 63 and 65 is 4095.
2. What are the Factors of 63?
Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.
3. What are the Factors of 65?
Answer: Factors of 65 are 1, 5, 13, 65. There are 4 integers that are factors of 65. The greatest factor of 65 is 65.
4. How to Find the LCM of 63 and 65?
Answer:
Least Common Multiple of 63 and 65 = 4095
Step 1: Find the prime factorization of 63
63 = 3 x 3 x 7
Step 2: Find the prime factorization of 65
65 = 5 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 4095 = 3 x 3 x 5 x 7 x 13
Step 4: Therefore, the least common multiple of 63 and 65 is 4095.