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Factors and multiplesArithmeticElementary schoolabout 0:36

Find the least common multiple of 14, 21: animated lesson

A narrated, step-by-step factors and multiples video lesson with captions. Final answer: 42.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.2 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Least common multiple
Find the least common multiple of 14, 21.
2. Step by step
1. $14 = 2 \times 7,\quad 21 = 3 \times 7$
  Prime factorization of each number
2. $\operatorname{lcm}(14, 21) = \frac{14 \times 21}{\gcd(14, 21)} = \frac{294}{7} = 42$
  Use the GCF to combine 14 and 21
3. $2 \times 3 \times 7 = 42$
  Confirm with prime factors
3. The answer
$42$
LCM(14, 21) = 42
4. Check
- 42 ÷ 14 = 3
- 42 ÷ 21 = 2

Transcript

The problem. Here is the problem: Find the least common multiple of 14, 21. Find the least common multiple of the numbers.

Step by step. Prime factorization of each number. Use the GCF to combine 14 and 21. Confirm with prime factors. Take every prime that appears, each with its largest exponent.

The answer. So the answer is 42. 42 is the smallest positive number that every input divides exactly.

Check. 42 divided by 14 equals 3. 42 divided by 21 equals 2.

About factors and multiples

Find greatest common factors and least common multiples using prime factorisation.

Find the least common multiple of 14, 21: Animated Lesson