Least Common Multiple (LCM) of 37 and 29
The least common multiple (LCM) of 37 and 29 is 1073.
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 37 and 29?
First, calculate the GCD of 37 and 29 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 29 = 1 remainder 8 |
| 2 | 29 ÷ 8 = 3 remainder 5 |
| 3 | 8 ÷ 5 = 1 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 42 | 966 |
| 174 and 108 | 3132 |
| 157 and 96 | 15072 |
| 45 and 174 | 2610 |
| 100 and 121 | 12100 |