Least Common Multiple (LCM) of 108 and 174
The least common multiple (LCM) of 108 and 174 is 3132.
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 108 and 174?
First, calculate the GCD of 108 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 174 = 0 remainder 108 |
| 2 | 174 ÷ 108 = 1 remainder 66 |
| 3 | 108 ÷ 66 = 1 remainder 42 |
| 4 | 66 ÷ 42 = 1 remainder 24 |
| 5 | 42 ÷ 24 = 1 remainder 18 |
| 6 | 24 ÷ 18 = 1 remainder 6 |
| 7 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 170 | 6970 |
| 196 and 194 | 19012 |
| 165 and 35 | 1155 |
| 161 and 68 | 10948 |
| 121 and 160 | 19360 |