Least Common Multiple (LCM) of 42 and 55
The least common multiple (LCM) of 42 and 55 is 2310.
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 42 and 55?
First, calculate the GCD of 42 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 55 = 0 remainder 42 |
| 2 | 55 ÷ 42 = 1 remainder 13 |
| 3 | 42 ÷ 13 = 3 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 53 | 10335 |
| 14 and 113 | 1582 |
| 17 and 10 | 170 |
| 109 and 63 | 6867 |
| 52 and 29 | 1508 |