Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 786 and 789 the smallest integer that is 206718 that is divisible by both numbers.
Least Common Multiple (LCM) of 786 and 789 is 206718.
LCM(786,789) = 206718
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 786 and 789. First we will calculate the prime factors of 786 and 789.
Prime Factorization of 786
2 | 786 |
3 | 393 |
131 | 131 |
1 |
Prime factors of 786 are 2, 3,131. Prime factorization of 786 in exponential form is:
786 = 21×31×1311
Prime Factorization of 789
3 | 789 |
263 | 263 |
1 |
Prime factors of 789 are 3,263. Prime factorization of 789 in exponential form is:
789 = 31×2631
Now multiplying the highest exponent prime factors to calculate the LCM of 786 and 789.
LCM(786,789) = 21×31×1311×2631
LCM(786,789) = 206718
Factors of 786
List of positive integer factors of 786 that divides 786 without a remainder.
1, 2, 3, 6, 131, 262, 393, 786
Factors of 789
List of positive integer factors of 789 that divides 789 without a remainder.
1, 3, 263, 789
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 786 and 789, than apply into the LCM equation.
GCF(786,789) = 3
LCM(786,789) = ( 786 × 789) / 3
LCM(786,789) = 620154 / 3
LCM(786,789) = 206718
(i) The LCM of 789 and 786 is associative
LCM of 786 and 789 = LCM of 789 and 786
1. What is the LCM of 786 and 789?
Answer: LCM of 786 and 789 is 206718.
2. What are the Factors of 786?
Answer: Factors of 786 are 1, 2, 3, 6, 131, 262, 393, 786. There are 8 integers that are factors of 786. The greatest factor of 786 is 786.
3. What are the Factors of 789?
Answer: Factors of 789 are 1, 3, 263, 789. There are 4 integers that are factors of 789. The greatest factor of 789 is 789.
4. How to Find the LCM of 786 and 789?
Answer:
Least Common Multiple of 786 and 789 = 206718
Step 1: Find the prime factorization of 786
786 = 2 x 3 x 131
Step 2: Find the prime factorization of 789
789 = 3 x 263
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 206718 = 2 x 3 x 131 x 263
Step 4: Therefore, the least common multiple of 786 and 789 is 206718.