Least Common Multiple (LCM) of 51 and 91
The least common multiple (LCM) of 51 and 91 is 4641.
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 51 and 91?
First, calculate the GCD of 51 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 91 = 0 remainder 51 |
| 2 | 91 ÷ 51 = 1 remainder 40 |
| 3 | 51 ÷ 40 = 1 remainder 11 |
| 4 | 40 ÷ 11 = 3 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 122 | 4148 |
| 118 and 181 | 21358 |
| 110 and 150 | 1650 |
| 134 and 107 | 14338 |
| 107 and 154 | 16478 |