Least Common Multiple (LCM) of 119 and 174
The least common multiple (LCM) of 119 and 174 is 20706.
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 119 and 174?
First, calculate the GCD of 119 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 174 = 0 remainder 119 |
| 2 | 174 ÷ 119 = 1 remainder 55 |
| 3 | 119 ÷ 55 = 2 remainder 9 |
| 4 | 55 ÷ 9 = 6 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 155 | 27435 |
| 138 and 10 | 690 |
| 160 and 51 | 8160 |
| 125 and 55 | 1375 |
| 196 and 112 | 784 |