Least Common Multiple (LCM) of 137 and 179
The least common multiple (LCM) of 137 and 179 is 24523.
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 179?
First, calculate the GCD of 137 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 179 = 0 remainder 137 |
| 2 | 179 ÷ 137 = 1 remainder 42 |
| 3 | 137 ÷ 42 = 3 remainder 11 |
| 4 | 42 ÷ 11 = 3 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 155 | 23715 |
| 52 and 158 | 4108 |
| 177 and 117 | 6903 |
| 159 and 29 | 4611 |
| 75 and 133 | 9975 |