Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 767 and 768 the smallest integer that is 589056 that is divisible by both numbers.
Least Common Multiple (LCM) of 767 and 768 is 589056.
LCM(767,768) = 589056
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 767 and 768. First we will calculate the prime factors of 767 and 768.
Prime Factorization of 767
13 | 767 |
59 | 59 |
1 |
Prime factors of 767 are 13,59. Prime factorization of 767 in exponential form is:
767 = 131×591
Prime Factorization of 768
2 | 768 |
2 | 384 |
2 | 192 |
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 768 are 2,3. Prime factorization of 768 in exponential form is:
768 = 28×31
Now multiplying the highest exponent prime factors to calculate the LCM of 767 and 768.
LCM(767,768) = 28×31×131×591
LCM(767,768) = 589056
Factors of 767
List of positive integer factors of 767 that divides 767 without a remainder.
1, 13, 59, 767
Factors of 768
List of positive integer factors of 768 that divides 768 without a remainder.
1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 767 and 768, than apply into the LCM equation.
GCF(767,768) = 1
LCM(767,768) = ( 767 × 768) / 1
LCM(767,768) = 589056 / 1
LCM(767,768) = 589056
(i) The LCM of 768 and 767 is associative
LCM of 767 and 768 = LCM of 768 and 767
1. What is the LCM of 767 and 768?
Answer: LCM of 767 and 768 is 589056.
2. What are the Factors of 767?
Answer: Factors of 767 are 1, 13, 59, 767. There are 4 integers that are factors of 767. The greatest factor of 767 is 767.
3. What are the Factors of 768?
Answer: Factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768. There are 18 integers that are factors of 768. The greatest factor of 768 is 768.
4. How to Find the LCM of 767 and 768?
Answer:
Least Common Multiple of 767 and 768 = 589056
Step 1: Find the prime factorization of 767
767 = 13 x 59
Step 2: Find the prime factorization of 768
768 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 589056 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 59
Step 4: Therefore, the least common multiple of 767 and 768 is 589056.