Least Common Multiple (LCM) of 137 and 176
The least common multiple (LCM) of 137 and 176 is 24112.
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 176?
First, calculate the GCD of 137 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 176 = 0 remainder 137 |
| 2 | 176 ÷ 137 = 1 remainder 39 |
| 3 | 137 ÷ 39 = 3 remainder 20 |
| 4 | 39 ÷ 20 = 1 remainder 19 |
| 5 | 20 ÷ 19 = 1 remainder 1 |
| 6 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 63 | 126 |
| 106 and 149 | 15794 |
| 160 and 129 | 20640 |
| 158 and 134 | 10586 |
| 19 and 19 | 19 |