Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 456 and 463 the smallest integer that is 211128 that is divisible by both numbers.
Least Common Multiple (LCM) of 456 and 463 is 211128.
LCM(456,463) = 211128
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 456 and 463. First we will calculate the prime factors of 456 and 463.
Prime Factorization of 456
2 | 456 |
2 | 228 |
2 | 114 |
3 | 57 |
19 | 19 |
1 |
Prime factors of 456 are 2, 3,19. Prime factorization of 456 in exponential form is:
456 = 23×31×191
Prime Factorization of 463
463 | 463 |
1 |
Prime factors of 463 are 463. Prime factorization of 463 in exponential form is:
463 = 4631
Now multiplying the highest exponent prime factors to calculate the LCM of 456 and 463.
LCM(456,463) = 23×31×191×4631
LCM(456,463) = 211128
Factors of 456
List of positive integer factors of 456 that divides 456 without a remainder.
1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
Factors of 463
List of positive integer factors of 463 that divides 463 without a remainder.
1, 463
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 456 and 463, than apply into the LCM equation.
GCF(456,463) = 1
LCM(456,463) = ( 456 × 463) / 1
LCM(456,463) = 211128 / 1
LCM(456,463) = 211128
(i) The LCM of 463 and 456 is associative
LCM of 456 and 463 = LCM of 463 and 456
1. What is the LCM of 456 and 463?
Answer: LCM of 456 and 463 is 211128.
2. What are the Factors of 456?
Answer: Factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456. There are 16 integers that are factors of 456. The greatest factor of 456 is 456.
3. What are the Factors of 463?
Answer: Factors of 463 are 1, 463. There are 2 integers that are factors of 463. The greatest factor of 463 is 463.
4. How to Find the LCM of 456 and 463?
Answer:
Least Common Multiple of 456 and 463 = 211128
Step 1: Find the prime factorization of 456
456 = 2 x 2 x 2 x 3 x 19
Step 2: Find the prime factorization of 463
463 = 463
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 211128 = 2 x 2 x 2 x 3 x 19 x 463
Step 4: Therefore, the least common multiple of 456 and 463 is 211128.