Least Common Multiple (LCM) of 118 and 174
The least common multiple (LCM) of 118 and 174 is 10266.
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 118 and 174?
First, calculate the GCD of 118 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 174 = 0 remainder 118 |
| 2 | 174 ÷ 118 = 1 remainder 56 |
| 3 | 118 ÷ 56 = 2 remainder 6 |
| 4 | 56 ÷ 6 = 9 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 24 | 168 |
| 188 and 165 | 31020 |
| 164 and 126 | 10332 |
| 157 and 68 | 10676 |
| 109 and 88 | 9592 |