Least Common Multiple (LCM) of 110 and 167
The least common multiple (LCM) of 110 and 167 is 18370.
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 110 and 167?
First, calculate the GCD of 110 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 167 = 0 remainder 110 |
| 2 | 167 ÷ 110 = 1 remainder 57 |
| 3 | 110 ÷ 57 = 1 remainder 53 |
| 4 | 57 ÷ 53 = 1 remainder 4 |
| 5 | 53 ÷ 4 = 13 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 167 | 9185 |
| 87 and 79 | 6873 |
| 145 and 80 | 2320 |
| 31 and 164 | 5084 |
| 80 and 47 | 3760 |