Least Common Multiple (LCM) of 91 and 149
The least common multiple (LCM) of 91 and 149 is 13559.
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 149?
First, calculate the GCD of 91 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 149 = 0 remainder 91 |
| 2 | 149 ÷ 91 = 1 remainder 58 |
| 3 | 91 ÷ 58 = 1 remainder 33 |
| 4 | 58 ÷ 33 = 1 remainder 25 |
| 5 | 33 ÷ 25 = 1 remainder 8 |
| 6 | 25 ÷ 8 = 3 remainder 1 |
| 7 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 126 | 2898 |
| 101 and 64 | 6464 |
| 132 and 138 | 3036 |
| 21 and 103 | 2163 |
| 109 and 120 | 13080 |