Least Common Multiple (LCM) of 45 and 74
The least common multiple (LCM) of 45 and 74 is 3330.
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 45 and 74?
First, calculate the GCD of 45 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 74 = 0 remainder 45 |
| 2 | 74 ÷ 45 = 1 remainder 29 |
| 3 | 45 ÷ 29 = 1 remainder 16 |
| 4 | 29 ÷ 16 = 1 remainder 13 |
| 5 | 16 ÷ 13 = 1 remainder 3 |
| 6 | 13 ÷ 3 = 4 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 79 | 5451 |
| 35 and 146 | 5110 |
| 42 and 174 | 1218 |
| 26 and 16 | 208 |
| 86 and 80 | 3440 |