mathpi.netIn this class, we will answer: What is the LCM of 21 and 50. Then, we shall present three different ways of finding the LCM of the given numbers in a step by step detailed calculation. The first is Division method, the second is Prime Factorization method, and the third is the Listing of Multiples.
Answer
LCM of 21 and 50 is 1050.
Inputs
LCM of 21 and 50 using Division Method
The following is the division table of 21 and 50 for finding the common factors, and the remaining factors.
| 2 | 21 | 50 |
| 3 | 21 | 25 |
| 5 | 7 | 25 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| 1 | 1 |
LCM = Product of factors (highlighted as bold in the first column)
LCM = 2×3×5×5×7 = 1050
LCM of 21 and 50 using Prime Factors
Step 1: Find the Prime Factors
Prime factors of 21 are : 3,7
Prime factors of 50 are : 2,5,5
Step 2: Identify Common Prime Factors
There are no common factors between 21 and 50. Therefore, we can skip the step of multiplying the common factors, and continue with the next step.
We can assume that, Product of Common Prime Factors = 1
Step 4: Multiply Remaining Prime Factors
Remaining prime factors of 21 are : 3, 7
Remaining prime factors of 50 are : 2, 5, 5
Multiply all these remaining prime factors to the result.
LCM = (Product of Common Prime Factors) × (Product of remaining prime factors of m) × (Product of remaining prime factors of n)
LCM = \(1×(3×7)×(2×5×5)\)
Step 5: Result
LCM = 1050
Therefore,
LCM(21, 50) = 1050
LCM of 21 and 50 using List of Multiples
The following table lists the multiples of 21 and 50.
| Multiples of 21 | 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, 315, 336, 357, 378, 399, 420, 441, 462, 483, 504, 525, 546, 567, 588, 609, 630, 651, 672, 693, 714, 735, 756, 777, 798, 819, 840, 861, 882, 903, 924, 945, 966, 987, 1008, 1029, 1050, 1071, 1092, ... |
| Multiples of 50 | 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 1000, 1050, 1100, 1150, ... |
Of the multiples listed for 21 and 50, 1050 is the common multiple and the least.
Therefore,
LCM(21, 50) = 1050