Least Common Multiple (LCM) of 174 and 154
The least common multiple (LCM) of 174 and 154 is 13398.
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 154?
First, calculate the GCD of 174 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 154 = 1 remainder 20 |
| 2 | 154 ÷ 20 = 7 remainder 14 |
| 3 | 20 ÷ 14 = 1 remainder 6 |
| 4 | 14 ÷ 6 = 2 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 114 | 7638 |
| 186 and 67 | 12462 |
| 32 and 114 | 1824 |
| 155 and 28 | 4340 |
| 164 and 25 | 4100 |