Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 81 and 78 the smallest integer that is 2106 that is divisible by both numbers.
Least Common Multiple (LCM) of 81 and 78 is 2106.
LCM(81,78) = 2106
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 81 and 78. First we will calculate the prime factors of 81 and 78.
Prime Factorization of 81
3 | 81 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 81 are 3. Prime factorization of 81 in exponential form is:
81 = 34
Prime Factorization of 78
2 | 78 |
3 | 39 |
13 | 13 |
1 |
Prime factors of 78 are 2, 3,13. Prime factorization of 78 in exponential form is:
78 = 21×31×131
Now multiplying the highest exponent prime factors to calculate the LCM of 81 and 78.
LCM(81,78) = 21×34×131
LCM(81,78) = 2106
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1, 3, 9, 27, 81
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1, 2, 3, 6, 13, 26, 39, 78
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 81 and 78, than apply into the LCM equation.
GCF(81,78) = 3
LCM(81,78) = ( 81 × 78) / 3
LCM(81,78) = 6318 / 3
LCM(81,78) = 2106
(i) The LCM of 78 and 81 is associative
LCM of 81 and 78 = LCM of 78 and 81
1. What is the LCM of 81 and 78?
Answer: LCM of 81 and 78 is 2106.
2. What are the Factors of 81?
Answer: Factors of 81 are 1, 3, 9, 27, 81. There are 5 integers that are factors of 81. The greatest factor of 81 is 81.
3. What are the Factors of 78?
Answer: Factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78. There are 8 integers that are factors of 78. The greatest factor of 78 is 78.
4. How to Find the LCM of 81 and 78?
Answer:
Least Common Multiple of 81 and 78 = 2106
Step 1: Find the prime factorization of 81
81 = 3 x 3 x 3 x 3
Step 2: Find the prime factorization of 78
78 = 2 x 3 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 = 2106 = 2 x 3 x 3 x 3 x 3 x 13
Step 4: Therefore, the least common multiple of 81 and 78 is 2106.