LCM of 78 and 95 = 7410
Quick Answer
LCM(78 and 95) = 7410. (78 and 95 are coprime, so LCM equals their product.)
First common multiples: 7410, 14820, 22230, 29640, 37050. Related GCF: 1.
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Step-by-Step: LCM via the GCF Identity
The fastest way to compute the LCM uses the identity LCM(a, b) × GCF(a, b) = a × b. So LCM = (a × b) / GCF. We first find the GCF with the Euclidean algorithm, then apply the identity.
Euclidean reduction for (78, 95):
| Step | Dividend ÷ Divisor | Quotient | Remainder |
|---|---|---|---|
| 1 | 95 ÷ 78 | 1 | 17 |
| 2 | 78 ÷ 17 | 4 | 10 |
| 3 | 17 ÷ 10 | 1 | 7 |
| 4 | 10 ÷ 7 | 1 | 3 |
| 5 | 7 ÷ 3 | 2 | 1 |
| 6 | 3 ÷ 1 | 3 | 0 |
GCF = 1. Applying the identity:
LCM = (78 × 95) ÷ GCF = 7410 ÷ 1 = 7410
LCM(78 and 95) = 7410
First 5 Common Multiples of 78 and 95
Every common multiple is a multiple of the LCM. The first five are:
| k | k × LCM | Value |
|---|---|---|
| 1 | 1 × 7410 | 7,410 |
| 2 | 2 × 7410 | 14,820 |
| 3 | 3 × 7410 | 22,230 |
| 4 | 4 × 7410 | 29,640 |
| 5 | 5 × 7410 | 37,050 |
Related: GCF of 78 and 95
GCF(78, 95) = 1
From the identity LCM × GCF = a × b:
7410 × 1 = 7410 = 78 × 95
Because the GCF equals 1, 78 and 95 are coprime (relatively prime). For coprime pairs, LCM always equals the product of the two numbers.
See the dedicated GCF of 78 and 95 page for the full common-divisor list and Euclidean walk-through.
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How to Find the Least Common Multiple
The Least Common Multiple (LCM) of two or more positive integers is the smallest positive integer divisible by each of them.
Method 1: GCF Identity (used above)
- Find the GCF (Greatest Common Factor) using the Euclidean algorithm.
- Apply the identity: LCM = (a × b) / GCF.
Method 2: Prime Factorization
- Find the prime factorization of each number.
- For each prime that appears in any factorization, take the highest exponent across all inputs.
- Multiply these prime powers together.
Example: LCM(12, 18) via prime factorization
- 12 = 2² × 3¹
- 18 = 2¹ × 3²
- Take the highest exponent of each prime: 2² (from 12), 3² (from 18).
- LCM = 2² × 3² = 4 × 9 = 36
Method 3: Listing Multiples
- List the multiples of each number until you find a common one.
- That smallest common multiple is the LCM.
This is the slowest method for large inputs; the GCF identity is preferred.
Nearby LCM Examples
| Pair | LCM | GCF |
|---|---|---|
| 75 and 100 | 300 | 25 |
| 72 and 96 | 288 | 24 |
| 60 and 90 | 180 | 30 |
| 45 and 60 | 180 | 15 |
| 100 and 150 | 300 | 50 |
| 36 and 48 | 144 | 12 |
Frequently Asked Questions
What is the LCM of 78 and 95?
LCM(78 and 95) = 7410. This is the smallest positive integer divisible by each input.
How is the LCM of 78 and 95 calculated?
Apply the identity LCM = (a × b) / GCF. For 78 and 95, GCF = 1, so LCM = 7410 / 1 = 7410.
Why does LCM(78 and 95) equal their product?
Because 78 and 95 are coprime (GCF = 1). Whenever two numbers share no common factor greater than 1, their least common multiple is just their product.
How are LCM and GCF related?
By the identity LCM(a, b) × GCF(a, b) = a × b. So once you have the GCF (via the Euclidean algorithm), the LCM follows immediately: LCM = (a × b) / GCF.
What is LCM used for?
Two major uses: (1) adding/subtracting fractions with different denominators (find the common denominator); (2) scheduling — when two repeating events occur together (every 12 days and every 18 days → coincide every LCM(12, 18) = 36 days).
Related Calculators
- GCF of 78 and 95 = 1
- Prime Factorization Calculator
- Divisors of a Number
- Multiples of a Number
- Fraction Calculator (uses LCM for common denominators)
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