Least Common Multiple (LCM) of 91 and 118
The least common multiple (LCM) of 91 and 118 is 10738.
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 118?
First, calculate the GCD of 91 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 118 = 0 remainder 91 |
| 2 | 118 ÷ 91 = 1 remainder 27 |
| 3 | 91 ÷ 27 = 3 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 55 | 660 |
| 74 and 138 | 5106 |
| 80 and 123 | 9840 |
| 172 and 51 | 8772 |
| 58 and 130 | 3770 |