Least Common Multiple (LCM) of 74 and 115
The least common multiple (LCM) of 74 and 115 is 8510.
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 74 and 115?
First, calculate the GCD of 74 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 115 = 0 remainder 74 |
| 2 | 115 ÷ 74 = 1 remainder 41 |
| 3 | 74 ÷ 41 = 1 remainder 33 |
| 4 | 41 ÷ 33 = 1 remainder 8 |
| 5 | 33 ÷ 8 = 4 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 138 | 10074 |
| 104 and 111 | 11544 |
| 32 and 140 | 1120 |
| 133 and 126 | 2394 |
| 171 and 93 | 5301 |