LCM (19,349,604; 96,748,020) = ? Calculate the least common multiple, LCM, by two methods: 1) Numbers' divisibility and 2) The prime factorization

lcm (19,349,604; 96,748,020) = ?

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:

96,748,020 ÷ 19,349,604 = 5 + 0

=> 96,748,020 = 19,349,604 × 5

=> 96,748,020 is divisible by 19,349,604.

=> 96,748,020 is a multiple of 19,349,604.

The smallest multiple of 96,748,020 is the number itself: 96,748,020.

The least common multiple:
lcm (19,349,604; 96,748,020) = 96,748,020

>> The divisibility of numbers

lcm (19,349,604; 96,748,020) = 96,748,020 = 2² × 3⁵ × 5 × 17 × 1,171
96,748,020 is a multiple of 19,349,604

Method 2. The prime factorization:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.

19,349,604 = 2² × 3⁵ × 17 × 1,171
19,349,604 is not a prime number but a composite one.

96,748,020 = 2² × 3⁵ × 5 × 17 × 1,171
96,748,020 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.

>> The prime factorization

Calculate the least common multiple, lcm:

Multiply all the prime factors of the two numbers, taken by the largest exponents (largest powers).

lcm (19,349,604; 96,748,020) = 2² × 3⁵ × 5 × 17 × 1,171

lcm (19,349,604; 96,748,020) = 2² × 3⁵ × 5 × 17 × 1,171 = 96,748,020
96,748,020 contains all the prime factors of the number 19,349,604

The final answer:
The least common multiple
lcm (19,349,604; 96,748,020) = 96,748,020 = 2² × 3⁵ × 5 × 17 × 1,171
96,748,020 is divisible by 19,349,604. 96,748,020 is a multiple of 19,349,604.
96,748,020 contains all the prime factors of the number 19,349,604

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:

lcm (19,349,604; 116,097,624) = ?

lcm (96,748,020; 580,488,120) = ?

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: the latest calculated

The LCM of 19,349,604 and 96,748,020 = ?	May 27 05:46 UTC (GMT)
The LCM of 33 and 35 = ?	May 27 05:46 UTC (GMT)
The LCM of 777 and 3,086 = ?	May 27 05:46 UTC (GMT)
The LCM of 894 and 2 = ?	May 27 05:45 UTC (GMT)
The LCM of 13 and 100,000 = ?	May 27 05:45 UTC (GMT)
The LCM of 27 and 35 = ?	May 27 05:45 UTC (GMT)
The LCM of 908 and 1,053 = ?	May 27 05:45 UTC (GMT)
The LCM of 1,311 and 74 = ?	May 27 05:45 UTC (GMT)
The LCM of 182 and 4 = ?	May 27 05:45 UTC (GMT)
The LCM of 28 and 64 = ?	May 27 05:45 UTC (GMT)
The LCM of 207 and 23 = ?	May 27 05:45 UTC (GMT)
The LCM of 28 and 5 = ?	May 27 05:45 UTC (GMT)
The LCM of 2,965 and 36 = ?	May 27 05:45 UTC (GMT)
The least common multiple, LCM: the list of all the operations

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
lcm (938, 982, 743) = 2 × 7 × 67 × 491 × 743 = 342,194,594

If two or more numbers have no common factors (they are coprime), then their least common multiple is calculated by simply multiplying the numbers.
Example:
6 = 2 × 3
35 = 5 × 7
lcm (6, 35) = 2 × 3 × 5 × 7 = 6 × 35 = 210

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples