Least Common Multiple of 90 and 91
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 90 and 91 the smallest integer that is 8190 that is divisible by both numbers.
Least Common Multiple (LCM) of 90 and 91 is 8190.
LCM(90,91) = 8190
LCM of 90 and 91
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 90 and 91 by Prime method
- Least Common Multiple of 90 and 91 with GCF Formula
LCM of 90 and 91 is 8190
Least common multiple can be found by multiplying the highest exponent prime factors of 90 and 91. First we will calculate the prime factors of 90 and 91.
Prime Factorization of 90
| 2 | 90 |
| 3 | 45 |
| 3 | 15 |
| 5 | 5 |
| 1 |
Prime factors of 90 are 2, 3,5. Prime factorization of 90 in exponential form is:
90 = 21×32×51
Prime Factorization of 91
| 7 | 91 |
| 13 | 13 |
| 1 |
Prime factors of 91 are 7,13. Prime factorization of 91 in exponential form is:
91 = 71×131
Now multiplying the highest exponent prime factors to calculate the LCM of 90 and 91.
LCM(90,91) = 21×32×51×71×131
LCM(90,91) = 8190
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Factors of 91
List of positive integer factors of 91 that divides 91 without a remainder.
1, 7, 13, 91
Least Common Multiple of 90 and 91 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 90 and 91, than apply into the LCM equation.
GCF(90,91) = 1
LCM(90,91) = ( 90 × 91) / 1
LCM(90,91) = 8190 / 1
LCM(90,91) = 8190
Properties of LCM 90 and 91
(i) The LCM of 91 and 90 is associative
LCM of 90 and 91 = LCM of 91 and 90
Related Least Common Multiples of 90
Related Least Common Multiples of 91
Frequently Asked Questions on LCM of 90 and 91
1. What is the LCM of 90 and 91?
Answer: LCM of 90 and 91 is 8190.
2. What are the Factors of 90?
Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.
3. What are the Factors of 91?
Answer: Factors of 91 are 1, 7, 13, 91. There are 4 integers that are factors of 91. The greatest factor of 91 is 91.
4. How to Find the LCM of 90 and 91?
Answer:
Least Common Multiple of 90 and 91 = 8190
Step 1: Find the prime factorization of 90
90 = 2 x 3 x 3 x 5
Step 2: Find the prime factorization of 91
91 = 7 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 = 8190 = 2 x 3 x 3 x 5 x 7 x 13
Step 4: Therefore, the least common multiple of 90 and 91 is 8190.
