Least Common Multiple (LCM) of 74 and 100
The least common multiple (LCM) of 74 and 100 is 3700.
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 100?
First, calculate the GCD of 74 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 100 = 0 remainder 74 |
| 2 | 100 ÷ 74 = 1 remainder 26 |
| 3 | 74 ÷ 26 = 2 remainder 22 |
| 4 | 26 ÷ 22 = 1 remainder 4 |
| 5 | 22 ÷ 4 = 5 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 133 | 3192 |
| 195 and 85 | 3315 |
| 31 and 28 | 868 |
| 31 and 151 | 4681 |
| 112 and 73 | 8176 |