Least Common Multiple (LCM) of 167 and 45
The least common multiple (LCM) of 167 and 45 is 7515.
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 45?
First, calculate the GCD of 167 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 45 = 3 remainder 32 |
| 2 | 45 ÷ 32 = 1 remainder 13 |
| 3 | 32 ÷ 13 = 2 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 183 | 20130 |
| 138 and 52 | 3588 |
| 119 and 14 | 238 |
| 106 and 130 | 6890 |
| 115 and 76 | 8740 |