Least Common Multiple (LCM) of 137 and 178
The least common multiple (LCM) of 137 and 178 is 24386.
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 178?
First, calculate the GCD of 137 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 178 = 0 remainder 137 |
| 2 | 178 ÷ 137 = 1 remainder 41 |
| 3 | 137 ÷ 41 = 3 remainder 14 |
| 4 | 41 ÷ 14 = 2 remainder 13 |
| 5 | 14 ÷ 13 = 1 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 15 | 300 |
| 18 and 13 | 234 |
| 158 and 93 | 14694 |
| 55 and 14 | 770 |
| 42 and 99 | 1386 |