Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1574 and 1576 the smallest integer that is 1240312 that is divisible by both numbers.
Least Common Multiple (LCM) of 1574 and 1576 is 1240312.
LCM(1574,1576) = 1240312
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 1574 and 1576. First we will calculate the prime factors of 1574 and 1576.
Prime Factorization of 1574
2 | 1574 |
787 | 787 |
1 |
Prime factors of 1574 are 2,787. Prime factorization of 1574 in exponential form is:
1574 = 21×7871
Prime Factorization of 1576
2 | 1576 |
2 | 788 |
2 | 394 |
197 | 197 |
1 |
Prime factors of 1576 are 2,197. Prime factorization of 1576 in exponential form is:
1576 = 23×1971
Now multiplying the highest exponent prime factors to calculate the LCM of 1574 and 1576.
LCM(1574,1576) = 23×1971×7871
LCM(1574,1576) = 1240312
Factors of 1574
List of positive integer factors of 1574 that divides 1574 without a remainder.
1, 2, 787, 1574
Factors of 1576
List of positive integer factors of 1576 that divides 1576 without a remainder.
1, 2, 4, 8, 197, 394, 788, 1576
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1574 and 1576, than apply into the LCM equation.
GCF(1574,1576) = 2
LCM(1574,1576) = ( 1574 × 1576) / 2
LCM(1574,1576) = 2480624 / 2
LCM(1574,1576) = 1240312
(i) The LCM of 1576 and 1574 is associative
LCM of 1574 and 1576 = LCM of 1576 and 1574
1. What is the LCM of 1574 and 1576?
Answer: LCM of 1574 and 1576 is 1240312.
2. What are the Factors of 1574?
Answer: Factors of 1574 are 1, 2, 787, 1574. There are 4 integers that are factors of 1574. The greatest factor of 1574 is 1574.
3. What are the Factors of 1576?
Answer: Factors of 1576 are 1, 2, 4, 8, 197, 394, 788, 1576. There are 8 integers that are factors of 1576. The greatest factor of 1576 is 1576.
4. How to Find the LCM of 1574 and 1576?
Answer:
Least Common Multiple of 1574 and 1576 = 1240312
Step 1: Find the prime factorization of 1574
1574 = 2 x 787
Step 2: Find the prime factorization of 1576
1576 = 2 x 2 x 2 x 197
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1240312 = 2 x 2 x 2 x 197 x 787
Step 4: Therefore, the least common multiple of 1574 and 1576 is 1240312.