Least Common Multiple (LCM) of 195 and 74
The least common multiple (LCM) of 195 and 74 is 14430.
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 195 and 74?
First, calculate the GCD of 195 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 74 = 2 remainder 47 |
| 2 | 74 ÷ 47 = 1 remainder 27 |
| 3 | 47 ÷ 27 = 1 remainder 20 |
| 4 | 27 ÷ 20 = 1 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 56 | 2520 |
| 150 and 133 | 19950 |
| 73 and 111 | 8103 |
| 138 and 45 | 2070 |
| 45 and 114 | 1710 |