Least Common Multiple (LCM) of 73 and 111
The least common multiple (LCM) of 73 and 111 is 8103.
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 73 and 111?
First, calculate the GCD of 73 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 73 ÷ 111 = 0 remainder 73 |
| 2 | 111 ÷ 73 = 1 remainder 38 |
| 3 | 73 ÷ 38 = 1 remainder 35 |
| 4 | 38 ÷ 35 = 1 remainder 3 |
| 5 | 35 ÷ 3 = 11 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 31 | 5642 |
| 187 and 176 | 2992 |
| 190 and 77 | 14630 |
| 135 and 77 | 10395 |
| 12 and 90 | 180 |