Least Common Multiple (LCM) of 61 and 74
The least common multiple (LCM) of 61 and 74 is 4514.
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 61 and 74?
First, calculate the GCD of 61 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 74 = 0 remainder 61 |
| 2 | 74 ÷ 61 = 1 remainder 13 |
| 3 | 61 ÷ 13 = 4 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 170 | 1530 |
| 122 and 23 | 2806 |
| 65 and 73 | 4745 |
| 39 and 105 | 1365 |
| 120 and 59 | 7080 |