Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 553 and 560 the smallest integer that is 44240 that is divisible by both numbers.
Least Common Multiple (LCM) of 553 and 560 is 44240.
LCM(553,560) = 44240
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 553 and 560. First we will calculate the prime factors of 553 and 560.
Prime Factorization of 553
7 | 553 |
79 | 79 |
1 |
Prime factors of 553 are 7,79. Prime factorization of 553 in exponential form is:
553 = 71×791
Prime Factorization of 560
2 | 560 |
2 | 280 |
2 | 140 |
2 | 70 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 560 are 2, 5,7. Prime factorization of 560 in exponential form is:
560 = 24×51×71
Now multiplying the highest exponent prime factors to calculate the LCM of 553 and 560.
LCM(553,560) = 24×51×71×791
LCM(553,560) = 44240
Factors of 553
List of positive integer factors of 553 that divides 553 without a remainder.
1, 7, 79, 553
Factors of 560
List of positive integer factors of 560 that divides 560 without a remainder.
1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 553 and 560, than apply into the LCM equation.
GCF(553,560) = 7
LCM(553,560) = ( 553 × 560) / 7
LCM(553,560) = 309680 / 7
LCM(553,560) = 44240
(i) The LCM of 560 and 553 is associative
LCM of 553 and 560 = LCM of 560 and 553
1. What is the LCM of 553 and 560?
Answer: LCM of 553 and 560 is 44240.
2. What are the Factors of 553?
Answer: Factors of 553 are 1, 7, 79, 553. There are 4 integers that are factors of 553. The greatest factor of 553 is 553.
3. What are the Factors of 560?
Answer: Factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560. There are 20 integers that are factors of 560. The greatest factor of 560 is 560.
4. How to Find the LCM of 553 and 560?
Answer:
Least Common Multiple of 553 and 560 = 44240
Step 1: Find the prime factorization of 553
553 = 7 x 79
Step 2: Find the prime factorization of 560
560 = 2 x 2 x 2 x 2 x 5 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 44240 = 2 x 2 x 2 x 2 x 5 x 7 x 79
Step 4: Therefore, the least common multiple of 553 and 560 is 44240.