Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 17233 and 17240 the smallest integer that is 297096920 that is divisible by both numbers.
Least Common Multiple (LCM) of 17233 and 17240 is 297096920.
LCM(17233,17240) = 297096920
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 17233 and 17240. First we will calculate the prime factors of 17233 and 17240.
Prime Factorization of 17233
19 | 17233 |
907 | 907 |
1 |
Prime factors of 17233 are 19,907. Prime factorization of 17233 in exponential form is:
17233 = 191×9071
Prime Factorization of 17240
2 | 17240 |
2 | 8620 |
2 | 4310 |
5 | 2155 |
431 | 431 |
1 |
Prime factors of 17240 are 2, 5,431. Prime factorization of 17240 in exponential form is:
17240 = 23×51×4311
Now multiplying the highest exponent prime factors to calculate the LCM of 17233 and 17240.
LCM(17233,17240) = 23×51×191×4311×9071
LCM(17233,17240) = 297096920
Factors of 17233
List of positive integer factors of 17233 that divides 17233 without a remainder.
1, 19, 907, 17233
Factors of 17240
List of positive integer factors of 17240 that divides 17240 without a remainder.
1, 2, 4, 5, 8, 10, 20, 40, 431, 862, 1724, 2155, 3448, 4310, 8620, 17240
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 17233 and 17240, than apply into the LCM equation.
GCF(17233,17240) = 1
LCM(17233,17240) = ( 17233 × 17240) / 1
LCM(17233,17240) = 297096920 / 1
LCM(17233,17240) = 297096920
(i) The LCM of 17240 and 17233 is associative
LCM of 17233 and 17240 = LCM of 17240 and 17233
1. What is the LCM of 17233 and 17240?
Answer: LCM of 17233 and 17240 is 297096920.
2. What are the Factors of 17233?
Answer: Factors of 17233 are 1, 19, 907, 17233. There are 4 integers that are factors of 17233. The greatest factor of 17233 is 17233.
3. What are the Factors of 17240?
Answer: Factors of 17240 are 1, 2, 4, 5, 8, 10, 20, 40, 431, 862, 1724, 2155, 3448, 4310, 8620, 17240. There are 16 integers that are factors of 17240. The greatest factor of 17240 is 17240.
4. How to Find the LCM of 17233 and 17240?
Answer:
Least Common Multiple of 17233 and 17240 = 297096920
Step 1: Find the prime factorization of 17233
17233 = 19 x 907
Step 2: Find the prime factorization of 17240
17240 = 2 x 2 x 2 x 5 x 431
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 297096920 = 2 x 2 x 2 x 5 x 19 x 431 x 907
Step 4: Therefore, the least common multiple of 17233 and 17240 is 297096920.