Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 462 and 470 the smallest integer that is 108570 that is divisible by both numbers.
Least Common Multiple (LCM) of 462 and 470 is 108570.
LCM(462,470) = 108570
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 462 and 470. First we will calculate the prime factors of 462 and 470.
Prime Factorization of 462
2 | 462 |
3 | 231 |
7 | 77 |
11 | 11 |
1 |
Prime factors of 462 are 2, 3, 7,11. Prime factorization of 462 in exponential form is:
462 = 21×31×71×111
Prime Factorization of 470
2 | 470 |
5 | 235 |
47 | 47 |
1 |
Prime factors of 470 are 2, 5,47. Prime factorization of 470 in exponential form is:
470 = 21×51×471
Now multiplying the highest exponent prime factors to calculate the LCM of 462 and 470.
LCM(462,470) = 21×31×51×71×111×471
LCM(462,470) = 108570
Factors of 462
List of positive integer factors of 462 that divides 462 without a remainder.
1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
Factors of 470
List of positive integer factors of 470 that divides 470 without a remainder.
1, 2, 5, 10, 47, 94, 235, 470
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 462 and 470, than apply into the LCM equation.
GCF(462,470) = 2
LCM(462,470) = ( 462 × 470) / 2
LCM(462,470) = 217140 / 2
LCM(462,470) = 108570
(i) The LCM of 470 and 462 is associative
LCM of 462 and 470 = LCM of 470 and 462
1. What is the LCM of 462 and 470?
Answer: LCM of 462 and 470 is 108570.
2. What are the Factors of 462?
Answer: Factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462. There are 16 integers that are factors of 462. The greatest factor of 462 is 462.
3. What are the Factors of 470?
Answer: Factors of 470 are 1, 2, 5, 10, 47, 94, 235, 470. There are 8 integers that are factors of 470. The greatest factor of 470 is 470.
4. How to Find the LCM of 462 and 470?
Answer:
Least Common Multiple of 462 and 470 = 108570
Step 1: Find the prime factorization of 462
462 = 2 x 3 x 7 x 11
Step 2: Find the prime factorization of 470
470 = 2 x 5 x 47
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 108570 = 2 x 3 x 5 x 7 x 11 x 47
Step 4: Therefore, the least common multiple of 462 and 470 is 108570.