Least Common Multiple (LCM) of 146 and 77
The least common multiple (LCM) of 146 and 77 is 11242.
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 146 and 77?
First, calculate the GCD of 146 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 77 = 1 remainder 69 |
| 2 | 77 ÷ 69 = 1 remainder 8 |
| 3 | 69 ÷ 8 = 8 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 160 | 1120 |
| 55 and 20 | 220 |
| 157 and 178 | 27946 |
| 41 and 34 | 1394 |
| 113 and 145 | 16385 |