Least Common Multiple (LCM) of 51 and 190
The least common multiple (LCM) of 51 and 190 is 9690.
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 190?
First, calculate the GCD of 51 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 190 = 0 remainder 51 |
| 2 | 190 ÷ 51 = 3 remainder 37 |
| 3 | 51 ÷ 37 = 1 remainder 14 |
| 4 | 37 ÷ 14 = 2 remainder 9 |
| 5 | 14 ÷ 9 = 1 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 57 | 8949 |
| 43 and 62 | 2666 |
| 76 and 144 | 2736 |
| 161 and 87 | 14007 |
| 109 and 81 | 8829 |