Calculate the Least (the Lowest) Common Multiple of Numbers, LCM, Using Two Methods: Either the Prime Factorization of Numbers, the Numbers' Divisibility, or the Euclidean Algorithm. Online Calculator

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 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