lcm (21,424; 107,120) = ?
Method 1. The divisibility of numbers:
A number 'a' is divisible by a number 'b' if there is no remainder when 'a' is divided by 'b'.
Divide the larger number by the smaller one.
When we divide our numbers, there is no remainder:
107,120 ÷ 21,424 = 5 + 0
=> 107,120 = 21,424 × 5
=> 107,120 is divisible by 21,424.
=> 107,120 is a multiple of 21,424.
The smallest multiple of 107,120 is the number itself: 107,120.
The least common multiple:
lcm (21,424; 107,120) = 107,120
lcm (21,424; 107,120) = 107,120 = 24 × 5 × 13 × 103
107,120 is a multiple of 21,424
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
21,424 = 24 × 13 × 103
21,424 is not a prime number but a composite one.
107,120 = 24 × 5 × 13 × 103
107,120 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.
Calculate the least common multiple, lcm:
Multiply all the prime factors of the two numbers, taken by the largest exponents (largest powers).
lcm (21,424; 107,120) = 24 × 5 × 13 × 103
lcm (21,424; 107,120) = 24 × 5 × 13 × 103 = 107,120
107,120 contains all the prime factors of the number 21,424
The final answer:
The least common multiple
lcm (21,424; 107,120) = 107,120 = 24 × 5 × 13 × 103
107,120 is divisible by 21,424. 107,120 is a multiple of 21,424.
107,120 contains all the prime factors of the number 21,424
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.
Other operations of this type:
Calculator: calculate the least common multiple, lcm