Least Common Multiple (LCM) of 54 and 196
The least common multiple (LCM) of 54 and 196 is 5292.
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 54 and 196?
First, calculate the GCD of 54 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 196 = 0 remainder 54 |
| 2 | 196 ÷ 54 = 3 remainder 34 |
| 3 | 54 ÷ 34 = 1 remainder 20 |
| 4 | 34 ÷ 20 = 1 remainder 14 |
| 5 | 20 ÷ 14 = 1 remainder 6 |
| 6 | 14 ÷ 6 = 2 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 83 | 14691 |
| 169 and 77 | 13013 |
| 41 and 26 | 1066 |
| 120 and 152 | 2280 |
| 113 and 106 | 11978 |