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 |
|---|---|
| 189 and 17 | 3213 |
| 140 and 14 | 140 |
| 176 and 132 | 528 |
| 128 and 28 | 896 |
| 192 and 67 | 12864 |