Least Common Multiple (LCM) of 91 and 99
The least common multiple (LCM) of 91 and 99 is 9009.
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 99?
First, calculate the GCD of 91 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 99 = 0 remainder 91 |
| 2 | 99 ÷ 91 = 1 remainder 8 |
| 3 | 91 ÷ 8 = 11 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 13 | 2041 |
| 113 and 39 | 4407 |
| 121 and 116 | 14036 |
| 153 and 56 | 8568 |
| 175 and 149 | 26075 |