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Worked Example • Multiples of 7

LCM of 14 and 21 (Equals 42)

The Least Common Multiple of 14 and 21 is 42. Both numbers sit in the 7-times table with GCF(14, 21) = 7, so LCM(14, 21) = (14 × 21) ÷ 7 = 42.

2 to 10 integers • up to 18 digits each
Parsed:1421
LCM of 14 and 21 Result
LCM(14, 21) = 42
Greatest Common Factor: GCF(14, 21) = 7
Check the answer (every division leaves a remainder of 0):
42 ÷ 14 = 342 ÷ 21 = 2

Show the Working (Step-by-Step)

Switch method in one click:

Step 1: Break each number down into its prime factors.

Write each input as a product of prime numbers, then group matching primes with exponents.

14 = 2 × 7
= 2 × 7
21 = 3 × 7
= 3 × 7

Step 2: For each prime, pick the highest exponent that appears in any single number.

PrimeIn 14In 21Highest Power
22¹—2¹ = 2
3—3¹3¹ = 3
77¹7¹7¹ = 7

Step 3: Multiply those highest prime powers together to get the LCM.

LCM = 2¹ × 3¹ × 7¹ = 2 × 3 × 7 = 42

Full Written Solution for the LCM of 14 and 21

If you are copying the steps onto a homework worksheet, here is how each method reaches LCM(14, 21) = 42:

Method A: Prime Factorization

  • • 14 = 2 × 7
  • • 21 = 3 × 7

Multiply the highest power of each prime: 2¹ × 3¹ × 7¹ = 42.

Method B: GCF & Exact Division Check

The Greatest Common Factor of 14 and 21 is 7.

42 ÷ 14 = 3 (remainder 0 ✓)
42 ÷ 21 = 2 (remainder 0 ✓)

Real-World & Fraction Context

A two-week (14-day) payroll cycle and a three-week (21-day) maintenance schedule fall on the exact same Friday every 42 days (6 weeks).

Mistake to Watch Out For

Because 7 is a slightly less obvious factor than 2 or 5, students sometimes assume 14 and 21 are coprime and multiply 14 × 21 = 294.