Least Common Multiple (LCM) of 42 and 73
The least common multiple (LCM) of 42 and 73 is 3066.
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 73?
First, calculate the GCD of 42 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 73 = 0 remainder 42 |
| 2 | 73 ÷ 42 = 1 remainder 31 |
| 3 | 42 ÷ 31 = 1 remainder 11 |
| 4 | 31 ÷ 11 = 2 remainder 9 |
| 5 | 11 ÷ 9 = 1 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 123 | 4551 |
| 113 and 59 | 6667 |
| 113 and 188 | 21244 |
| 183 and 75 | 4575 |
| 86 and 173 | 14878 |