Least Common Multiple (LCM) of 137 and 174
The least common multiple (LCM) of 137 and 174 is 23838.
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 137 and 174?
First, calculate the GCD of 137 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 174 = 0 remainder 137 |
| 2 | 174 ÷ 137 = 1 remainder 37 |
| 3 | 137 ÷ 37 = 3 remainder 26 |
| 4 | 37 ÷ 26 = 1 remainder 11 |
| 5 | 26 ÷ 11 = 2 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 23 and 101 | 2323 |
| 77 and 35 | 385 |
| 178 and 175 | 31150 |
| 118 and 67 | 7906 |
| 106 and 83 | 8798 |