Calculate LCM (78,100; 999,999,999,993), the Least (Lowest) Common Multiple of the Numbers. Online Calculator

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

78,100 = 2² × 5² × 11 × 71
78,100 is not a prime number but a composite one.

999,999,999,993 = 3 × 19 × 83 × 211,371,803
999,999,999,993 is not a prime number but a composite one.

» Online calculator. Check whether a number is prime or not. The prime factorization of composite numbers

* Prime number: a natural number that is only divisible by 1 and itself. A prime number has exactly two factors: 1 and itself.
* Composite number: 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).

This algorithm involves the process of dividing numbers and calculating the remainders.

'a' and 'b' are the two natural numbers, 'a' >= 'b'.

Divide 'a' by 'b' and get the remainder of the operation, 'r'.

If 'r' = 0, STOP. 'b' = the gcf (hcf, gcd) of 'a' and 'b'.

Else: Replace ('a' by 'b') and ('b' by 'r'). Return to the step above.

Step 1. Divide the larger number by the smaller one:
999,999,999,993 ÷ 78,100 = 12,804,097 + 24,293

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Step 2. Divide the smaller number by the above operation's remainder:
78,100 ÷ 24,293 = 3 + 5,221

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Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
24,293 ÷ 5,221 = 4 + 3,409

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Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
5,221 ÷ 3,409 = 1 + 1,812

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Step 5. Divide the remainder of the step 3 by the remainder of the step 4:
3,409 ÷ 1,812 = 1 + 1,597

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Step 6. Divide the remainder of the step 4 by the remainder of the step 5:
1,812 ÷ 1,597 = 1 + 215

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Step 7. Divide the remainder of the step 5 by the remainder of the step 6:
1,597 ÷ 215 = 7 + 92

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Step 8. Divide the remainder of the step 6 by the remainder of the step 7:
215 ÷ 92 = 2 + 31

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Step 9. Divide the remainder of the step 7 by the remainder of the step 8:
92 ÷ 31 = 2 + 30

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Step 10. Divide the remainder of the step 8 by the remainder of the step 9:
31 ÷ 30 = 1 + 1

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Step 11. Divide the remainder of the step 9 by the remainder of the step 10:
30 ÷ 1 = 30 + 0

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At this step, the remainder is zero, so we stop:
1 is the number we were looking for - the last non-zero remainder.
This is the greatest (highest) common factor (divisor).

The greatest (highest) common factor (divisor):
gcf, hcf, gcd (78,100; 999,999,999,993) = 1

The least common multiple, Formula:

lcm (a; b) = ^{(a × b)} / _{gcf, hcf, gcd (a; b)}

» The Euclidean Algorithm

Why is it useful to calculate the least common multiple?

In order to add, subtract or sort fractions with different denominators, we must make their denominators the same. An easy way is to calculate the least common multiple of all the denominators (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.