Least Common Multiple (LCM) of 154 and 170
The least common multiple (LCM) of 154 and 170 is 13090.
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 170?
First, calculate the GCD of 154 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 170 = 0 remainder 154 |
| 2 | 170 ÷ 154 = 1 remainder 16 |
| 3 | 154 ÷ 16 = 9 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 66 | 1650 |
| 136 and 105 | 14280 |
| 195 and 131 | 25545 |
| 55 and 175 | 1925 |
| 45 and 156 | 2340 |