Least Common Multiple (LCM) of 101 and 154
The least common multiple (LCM) of 101 and 154 is 15554.
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 101 and 154?
First, calculate the GCD of 101 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 154 = 0 remainder 101 |
| 2 | 154 ÷ 101 = 1 remainder 53 |
| 3 | 101 ÷ 53 = 1 remainder 48 |
| 4 | 53 ÷ 48 = 1 remainder 5 |
| 5 | 48 ÷ 5 = 9 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 110 | 2530 |
| 90 and 136 | 6120 |
| 110 and 142 | 7810 |
| 178 and 39 | 6942 |
| 70 and 20 | 140 |