Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 84 and 89 the smallest integer that is 7476 that is divisible by both numbers.
Least Common Multiple (LCM) of 84 and 89 is 7476.
LCM(84,89) = 7476
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 84 and 89. First we will calculate the prime factors of 84 and 89.
Prime Factorization of 84
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 84 are 2, 3,7. Prime factorization of 84 in exponential form is:
84 = 22×31×71
Prime Factorization of 89
89 | 89 |
1 |
Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:
89 = 891
Now multiplying the highest exponent prime factors to calculate the LCM of 84 and 89.
LCM(84,89) = 22×31×71×891
LCM(84,89) = 7476
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 89
List of positive integer factors of 89 that divides 89 without a remainder.
1, 89
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 84 and 89, than apply into the LCM equation.
GCF(84,89) = 1
LCM(84,89) = ( 84 × 89) / 1
LCM(84,89) = 7476 / 1
LCM(84,89) = 7476
(i) The LCM of 89 and 84 is associative
LCM of 84 and 89 = LCM of 89 and 84
1. What is the LCM of 84 and 89?
Answer: LCM of 84 and 89 is 7476.
2. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
3. What are the Factors of 89?
Answer: Factors of 89 are 1, 89. There are 2 integers that are factors of 89. The greatest factor of 89 is 89.
4. How to Find the LCM of 84 and 89?
Answer:
Least Common Multiple of 84 and 89 = 7476
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 89
89 = 89
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 7476 = 2 x 2 x 3 x 7 x 89
Step 4: Therefore, the least common multiple of 84 and 89 is 7476.