Least Common Multiple (LCM) of 74 and 120
The least common multiple (LCM) of 74 and 120 is 4440.
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 120?
First, calculate the GCD of 74 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 120 = 0 remainder 74 |
| 2 | 120 ÷ 74 = 1 remainder 46 |
| 3 | 74 ÷ 46 = 1 remainder 28 |
| 4 | 46 ÷ 28 = 1 remainder 18 |
| 5 | 28 ÷ 18 = 1 remainder 10 |
| 6 | 18 ÷ 10 = 1 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 109 | 10682 |
| 15 and 135 | 135 |
| 39 and 165 | 2145 |
| 157 and 83 | 13031 |
| 123 and 59 | 7257 |