Least Common Multiple (LCM) of 115 and 174
The least common multiple (LCM) of 115 and 174 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 115 and 174?
First, calculate the GCD of 115 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 174 = 0 remainder 115 |
| 2 | 174 ÷ 115 = 1 remainder 59 |
| 3 | 115 ÷ 59 = 1 remainder 56 |
| 4 | 59 ÷ 56 = 1 remainder 3 |
| 5 | 56 ÷ 3 = 18 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 89 | 6942 |
| 83 and 178 | 14774 |
| 146 and 143 | 20878 |
| 101 and 143 | 14443 |
| 138 and 123 | 5658 |