Least Common Multiple (LCM) of 91 and 110
The least common multiple (LCM) of 91 and 110 is 10010.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 91 and 110?
First, calculate the GCD of 91 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 110 = 0 remainder 91 |
| 2 | 110 ÷ 91 = 1 remainder 19 |
| 3 | 91 ÷ 19 = 4 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 174 | 7830 |
| 163 and 82 | 13366 |
| 59 and 13 | 767 |
| 85 and 117 | 9945 |
| 180 and 25 | 900 |