Least Common Multiple (LCM) of 174 and 115
The least common multiple (LCM) of 174 and 115 is 20010.
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 174 and 115?
First, calculate the GCD of 174 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 115 = 1 remainder 59 |
| 2 | 115 ÷ 59 = 1 remainder 56 |
| 3 | 59 ÷ 56 = 1 remainder 3 |
| 4 | 56 ÷ 3 = 18 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 182 | 1638 |
| 176 and 181 | 31856 |
| 181 and 90 | 16290 |
| 81 and 185 | 14985 |
| 124 and 107 | 13268 |