Least Common Multiple (LCM) of 51 and 167
The least common multiple (LCM) of 51 and 167 is 8517.
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 167?
First, calculate the GCD of 51 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 167 = 0 remainder 51 |
| 2 | 167 ÷ 51 = 3 remainder 14 |
| 3 | 51 ÷ 14 = 3 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 121 | 19481 |
| 36 and 72 | 72 |
| 19 and 193 | 3667 |
| 46 and 64 | 1472 |
| 20 and 109 | 2180 |