How do you find the LCD of 3 and 6 step by step?

Factor each number into primes — 3 = 3, 6 = 2 × 3 — then take the highest power of every prime that appears and multiply them: 2 × 3 = 6. Listing multiples and the formula (product ÷ GCD) give the same 6.

Is the LCD of 3 and 6 the same as the LCM of 3 and 6?

Yes. The least common denominator is the least common multiple applied to denominators, so LCM(3, 6) = 6 as well. The two names describe the same number; only the context differs.

What is the LCD of 6 and 3?

It is the same number: 6. The least common denominator does not depend on the order you write the numbers in, so the LCD of 6 and 3 and the LCD of 3 and 6 are both 6.

How do you add 1/3 and 1/6?

Rewrite each fraction over 6: 1/3 = 2/6, 1/6 = 1/6. Then add the numerators only — 2/6 + 1/6 = 3/6, which simplifies to 1/2.

Why isn't the LCD of 3 and 6 18?

18 is a common denominator — multiplying the numbers always gives one — but it is not the least. 3 and 6 share a factor of 3, so 18 counts that factor more than once. Dividing it out gives 18 ÷ 3 = 6, the true LCD.

Do you have to use the least common denominator for 3 and 6?

No — any common denominator gives a correct answer, and 18 always works. But 6 keeps the numerators as small as possible, which usually means less simplifying at the end, so it is the one to reach for.

Least common denominator

LCD of 3 and 6

The least common denominator of 3 and 6 is 6. It is the smallest whole number 3 and 6 all divide into evenly — the denominator you put these fractions over before adding, subtracting, or comparing them. 6 is already a multiple of 3, so 6 is itself the common denominator — nothing larger is needed.

LCD of 3, 6 · also written LCD of 6 and 3

The least common denominator of 3 and 6 is 6.

2 × 3 = 6

3 × 6 ÷ 3 = 6

6 ÷ 3 = 2 · 6 ÷ 6 = 1

Enter your denominators

Type each denominator. We find the smallest number every one divides into.

Least common denominator

LCD of 3, 6 = LCM of 3, 6

Built from prime powers

2 × 3 = 6

Each number into the LCD

3× 2 =6
6× 1 =6

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The working

Three ways to reach 6

Listing multiples, prime factorisation, and the GCD formula are the three standard hand methods. All three land on 6 for 3 and 6 — pick whichever you were taught.

1
List the multiples
Write out the multiples of each number and stop at the first one they all share. That first shared multiple is the least common denominator.
3: 3, 6
6: 6
first shared multiple = 6
2
Prime factorisation
Break each number into primes, then take the highest power of every prime that appears anywhere and multiply those together. This is the method that scales to three or more denominators.
3 = 3
6 = 2 × 3
highest powers = 2 × 3 = 6
3
The GCD formula
Multiply the numbers, then divide by their greatest common divisor. The division removes the factor that was counted twice, leaving the least common denominator rather than just a common one.
3 × 6 = 18
GCD(3, 6) = 3
18 ÷ 3 = 6

Using it

Rewriting fractions over 6

The LCD is only worth finding because of what comes next. Multiply each fraction’s top and bottom by the factor that turns its denominator into 6 — the value does not change, only the way it is written.

Denominator	Multiply by	Over the LCD
3	× 2	n/3 → 2n/6
6	× 1	n/6 → n/6

Worked addition

1/3 + 1/6

= 2/6 + 1/6

= 3/6 = 1/2

Once every fraction sits over 6 the pieces are the same size, so you add the numerators and leave the denominator alone.

How this works

Why 3 and 6 gives 6

6 is already a multiple of 3, so 6 is itself the common denominator — nothing larger is needed.

One divides the other

The shape of this pair

When one denominator divides the other exactly, the larger one is already a common denominator — and since the LCD can never be smaller than the largest input, it is the least one too. No factorising required.

LCD ≥ 6

It can never be smaller

The least common denominator has to be divisible by every number in the set, so it can never fall below the largest of them. Anything smaller would leave at least one denominator unable to divide it evenly.

order does not matter

Reversing the numbers changes nothing

The LCD of 6 and 3 is the same 6. Least common multiples are commutative, so you can write the set in any order and the answer is unchanged.

change one number

What happens if the numbers change

Swapping a denominator for a multiple of itself often leaves the LCD alone; introducing a new prime always multiplies it up. The calculator above is prefilled with 3 and 6 — edit either box to see the effect immediately.

FAQ

LCD of 3 and 6 — common questions

The least common denominator of 3 and 6 is 6. It is the smallest whole number that 3 and 6 all divide into evenly, which makes it the denominator you rewrite these fractions over before adding, subtracting, or comparing them.