Least Common Multiple (LCM) of 167 and 120
The least common multiple (LCM) of 167 and 120 is 20040.
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 120?
First, calculate the GCD of 167 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 120 = 1 remainder 47 |
| 2 | 120 ÷ 47 = 2 remainder 26 |
| 3 | 47 ÷ 26 = 1 remainder 21 |
| 4 | 26 ÷ 21 = 1 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 192 | 12864 |
| 63 and 183 | 3843 |
| 29 and 77 | 2233 |
| 126 and 26 | 1638 |
| 135 and 51 | 2295 |