Least Common Multiple (LCM) of 154 and 174
The least common multiple (LCM) of 154 and 174 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 154 and 174?
First, calculate the GCD of 154 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 174 = 0 remainder 154 |
| 2 | 174 ÷ 154 = 1 remainder 20 |
| 3 | 154 ÷ 20 = 7 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 59 | 4543 |
| 119 and 112 | 1904 |
| 43 and 102 | 4386 |
| 110 and 68 | 3740 |
| 18 and 121 | 2178 |