Least Common Multiple (LCM) of 74 and 136
The least common multiple (LCM) of 74 and 136 is 5032.
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 136?
First, calculate the GCD of 74 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 136 = 0 remainder 74 |
| 2 | 136 ÷ 74 = 1 remainder 62 |
| 3 | 74 ÷ 62 = 1 remainder 12 |
| 4 | 62 ÷ 12 = 5 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 21 | 1785 |
| 167 and 69 | 11523 |
| 159 and 105 | 5565 |
| 23 and 58 | 1334 |
| 136 and 19 | 2584 |