Least Common Multiple (LCM) of 101 and 74
The least common multiple (LCM) of 101 and 74 is 7474.
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 74?
First, calculate the GCD of 101 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 74 = 1 remainder 27 |
| 2 | 74 ÷ 27 = 2 remainder 20 |
| 3 | 27 ÷ 20 = 1 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 86 | 10406 |
| 164 and 52 | 2132 |
| 177 and 69 | 4071 |
| 136 and 172 | 5848 |
| 160 and 84 | 3360 |