Least Common Multiple (LCM) of 155 and 196
The least common multiple (LCM) of 155 and 196 is 30380.
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 155 and 196?
First, calculate the GCD of 155 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 155 ÷ 196 = 0 remainder 155 |
| 2 | 196 ÷ 155 = 1 remainder 41 |
| 3 | 155 ÷ 41 = 3 remainder 32 |
| 4 | 41 ÷ 32 = 1 remainder 9 |
| 5 | 32 ÷ 9 = 3 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 137 | 12330 |
| 152 and 117 | 17784 |
| 160 and 170 | 2720 |
| 145 and 149 | 21605 |
| 14 and 115 | 1610 |