Least Common Multiple (LCM) of 167 and 51
The least common multiple (LCM) of 167 and 51 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 167 and 51?
First, calculate the GCD of 167 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 51 = 3 remainder 14 |
| 2 | 51 ÷ 14 = 3 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 90 | 360 |
| 170 and 152 | 12920 |
| 199 and 107 | 21293 |
| 87 and 32 | 2784 |
| 55 and 78 | 4290 |