Least Common Multiple (LCM) of 137 and 71
The least common multiple (LCM) of 137 and 71 is 9727.
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 71?
First, calculate the GCD of 137 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 71 = 1 remainder 66 |
| 2 | 71 ÷ 66 = 1 remainder 5 |
| 3 | 66 ÷ 5 = 13 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 143 and 152 | 21736 |
| 195 and 195 | 195 |
| 47 and 144 | 6768 |
| 144 and 114 | 2736 |
| 178 and 44 | 3916 |