Least Common Multiple (LCM) of 29 and 42
The least common multiple (LCM) of 29 and 42 is 1218.
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 42?
First, calculate the GCD of 29 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 29 ÷ 42 = 0 remainder 29 |
| 2 | 42 ÷ 29 = 1 remainder 13 |
| 3 | 29 ÷ 13 = 2 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 10 | 1270 |
| 88 and 44 | 88 |
| 114 and 69 | 2622 |
| 78 and 53 | 4134 |
| 100 and 157 | 15700 |