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 |
|---|---|
| 167 and 90 | 15030 |
| 153 and 127 | 19431 |
| 149 and 187 | 27863 |
| 161 and 52 | 8372 |
| 135 and 29 | 3915 |