Least Common Multiple (LCM) of 119 and 167
The least common multiple (LCM) of 119 and 167 is 19873.
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 119 and 167?
First, calculate the GCD of 119 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 167 = 0 remainder 119 |
| 2 | 167 ÷ 119 = 1 remainder 48 |
| 3 | 119 ÷ 48 = 2 remainder 23 |
| 4 | 48 ÷ 23 = 2 remainder 2 |
| 5 | 23 ÷ 2 = 11 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 89 | 13884 |
| 77 and 106 | 8162 |
| 45 and 58 | 2610 |
| 152 and 162 | 12312 |
| 187 and 68 | 748 |