Least Common Multiple (LCM) of 67 and 152
The least common multiple (LCM) of 67 and 152 is 10184.
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 67 and 152?
First, calculate the GCD of 67 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 152 = 0 remainder 67 |
| 2 | 152 ÷ 67 = 2 remainder 18 |
| 3 | 67 ÷ 18 = 3 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 40 | 720 |
| 49 and 43 | 2107 |
| 188 and 55 | 10340 |
| 100 and 172 | 4300 |
| 68 and 155 | 10540 |