Least Common Multiple (LCM) of 29 and 137
The least common multiple (LCM) of 29 and 137 is 3973.
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 29 and 137?
First, calculate the GCD of 29 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 137 = 0 remainder 29 |
| 2 | 137 ÷ 29 = 4 remainder 21 |
| 3 | 29 ÷ 21 = 1 remainder 8 |
| 4 | 21 ÷ 8 = 2 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 52 | 2132 |
| 46 and 178 | 4094 |
| 60 and 188 | 2820 |
| 58 and 119 | 6902 |
| 121 and 48 | 5808 |