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:
4,450 ÷ 10 = 445 + 0
=> 4,450 = 10 × 445
=> 4,450 is divisible by 10.
=> 4,450 is a multiple of 10.
The smallest multiple of 4,450 is the number itself: 4,450.
The least common multiple:
lcm (10; 4,450) = 4,450
lcm (10; 4,450) = 4,450 = 2 × 52 × 89
4,450 is a multiple of 10
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
4,450 = 2 × 52 × 89
4,450 is not a prime number but a composite one.
10 = 2 × 5
10 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 (4,450; 10) = 2 × 52 × 89
lcm (4,450; 10) = 2 × 52 × 89 = 4,450
4,450 contains all the prime factors of the number 10
The final answer:
The least common multiple
lcm (4,450; 10) = 4,450 = 2 × 52 × 89
4,450 is divisible by 10. 4,450 is a multiple of 10.
4,450 contains all the prime factors of the number 10
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.