Least Common Multiple (LCM) of 40 and 196
The least common multiple (LCM) of 40 and 196 is 1960.
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 40 and 196?
First, calculate the GCD of 40 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 196 = 0 remainder 40 |
| 2 | 196 ÷ 40 = 4 remainder 36 |
| 3 | 40 ÷ 36 = 1 remainder 4 |
| 4 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 175 | 25900 |
| 131 and 158 | 20698 |
| 116 and 147 | 17052 |
| 160 and 199 | 31840 |
| 104 and 153 | 15912 |