The least common multiple: lcm (62,640; 375,840) = 375,840 = 25 × 34 × 5 × 29 375,840 is a multiple of 62,640 Scroll down for the 2nd method...
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
62,640 = 24 × 33 × 5 × 29 62,640 is not a prime number but a composite one.
375,840 = 25 × 34 × 5 × 29 375,840 is not a prime number but a composite one.
* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself. * A composite number is a natural number that has at least one other factor than 1 and itself.
Multiply all the prime factors of the two numbers. If there are common prime factors then only the ones with the largest exponents are taken (the largest powers).
The least common multiple: lcm (62,640; 375,840) = 25 × 34 × 5 × 29 = 375,840 375,840 contains all the prime factors of the number 62,640
Why is it useful to calculate the least common multiple?
When adding, subtracting or sorting fractions with different denominators, in order to work with those fractions we must first make the denominators the same. An easy way is to calculate the least common multiple of all the denominators of the fractions (the least common denominator).
By definition, the least common multiple of two numbers is the smallest natural number that is: (1) greater than 0 and (2) a multiple of both numbers.
The least common multiple, LCM: the latest 5 calculated values
Calculator: calculate the least common multiple, lcm
Calculate the least common multiple of the numbers, LCM:
Method 1: Run the prime factorization of the numbers - then multiply all the prime factors of the numbers, taken by the largest exponents.
Method 2: The Euclidean algorithm: lcm (a; b) = (a × b) / gcf (a; b)
Method 3: The divisibility of the numbers.
The least common multiple (lcm). What it is and how to calculate it.
The number 60 is a common multiple of the numbers 6 and 15 because 60 is a multiple of 6 (60 = 6 × 10) and also a multiple of 15 (60 = 15 × 4).
There are infinitely many common multiples of 6 and 15.
If the number "v" is a multiple of the numbers "a" and "b", then all the multiples of "v" are also multiples of "a" and "b".
The common multiples of 6 and 15 are the numbers 30, 60, 90, 120, and so on.
Out of these, 30 is the smallest, 30 is the least common multiple (lcm) of 6 and 15.
Note: The prime factorization of a number: finding the prime numbers that multiply together to give that number.
If e = lcm (a, b), then the prime factorization of "e" must contain all the prime factors involved in the prime factorization of "a" and "b" taken by the highest power.
Example:
40 = 23 × 5
36 = 22 × 32
126 = 2 × 32 × 7
lcm (40, 36, 126) = 23 × 32 × 5 × 7 = 2,520
Note: 23 = 2 × 2 × 2 = 8. We are saying that 2 was raised to the power of 3. Or, shorter, 2 to the power of 3. In this example 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 23 is the power and 8 is the value of the power:
Another example of calculating the least common multiple, lcm:
938 = 2 × 7 × 67
982 = 2 × 491
743 = is a prime number and cannot be broken down into other prime factors