Least Common Multiple (LCM) of 152 and 194
The least common multiple (LCM) of 152 and 194 is 14744.
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 152 and 194?
First, calculate the GCD of 152 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 194 = 0 remainder 152 |
| 2 | 194 ÷ 152 = 1 remainder 42 |
| 3 | 152 ÷ 42 = 3 remainder 26 |
| 4 | 42 ÷ 26 = 1 remainder 16 |
| 5 | 26 ÷ 16 = 1 remainder 10 |
| 6 | 16 ÷ 10 = 1 remainder 6 |
| 7 | 10 ÷ 6 = 1 remainder 4 |
| 8 | 6 ÷ 4 = 1 remainder 2 |
| 9 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 98 | 1960 |
| 112 and 22 | 1232 |
| 52 and 192 | 2496 |
| 162 and 71 | 11502 |
| 200 and 125 | 1000 |