Least Common Multiple (LCM) of 29 and 196
The least common multiple (LCM) of 29 and 196 is 5684.
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 196?
First, calculate the GCD of 29 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 196 = 0 remainder 29 |
| 2 | 196 ÷ 29 = 6 remainder 22 |
| 3 | 29 ÷ 22 = 1 remainder 7 |
| 4 | 22 ÷ 7 = 3 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 111 | 1332 |
| 90 and 61 | 5490 |
| 185 and 102 | 18870 |
| 106 and 164 | 8692 |
| 100 and 57 | 5700 |