Least Common Multiple (LCM) of 51 and 191
The least common multiple (LCM) of 51 and 191 is 9741.
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 191?
First, calculate the GCD of 51 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 191 = 0 remainder 51 |
| 2 | 191 ÷ 51 = 3 remainder 38 |
| 3 | 51 ÷ 38 = 1 remainder 13 |
| 4 | 38 ÷ 13 = 2 remainder 12 |
| 5 | 13 ÷ 12 = 1 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 51 | 9843 |
| 177 and 63 | 3717 |
| 149 and 139 | 20711 |
| 138 and 82 | 5658 |
| 47 and 186 | 8742 |