Least Common Multiple (LCM) of 53 and 154
The least common multiple (LCM) of 53 and 154 is 8162.
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 53 and 154?
First, calculate the GCD of 53 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 154 = 0 remainder 53 |
| 2 | 154 ÷ 53 = 2 remainder 48 |
| 3 | 53 ÷ 48 = 1 remainder 5 |
| 4 | 48 ÷ 5 = 9 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 |
|---|---|
| 77 and 16 | 1232 |
| 120 and 142 | 8520 |
| 98 and 87 | 8526 |
| 195 and 19 | 3705 |
| 189 and 71 | 13419 |