LCM for 32, 48 and 64
What's the Least Common Multiple (LCM) of 32, 48 and 64?
Answer
(One hundred ninety-two)
192 is the smallest positive integer that 32, 48 and 64 all divide without a remainder — every other common multiple of the three is a multiple of it.
Finding the LCM of 32, 48 and 64 by Prime Factorization
Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:
All Prime Factors of 32: 2 × 2 × 2 × 2 × 2 (exponent form: 25)
All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)
All Prime Factors of 64: 2 × 2 × 2 × 2 × 2 × 2 (exponent form: 26)
| Prime factor | 32 | 48 | 64 | Highest power |
|---|---|---|---|---|
| 2 | 25 | 24 | 26 | 26 |
| 3 | — | 3 | — | 3 |
LCM = 26 × 3 = 192
Checking the LCM of 32, 48 and 64 Two Numbers at a Time
The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:
LCM(a, b) = (a × b) ÷ GCD(a, b)
LCM(32, 48) = (32 × 48) ÷ 16 = 1,536 ÷ 16 = 96
LCM(96, 64) = (96 × 64) ÷ 32 = 6,144 ÷ 32 = 192
LCM(32, 48, 64) = 192
The pairs may be taken in any order — 48 and 64 first, then 32 — and the answer is the same 192. That is exactly why the two routes on this page agree.
Related Calculations
See Also
- Greatest Common Factor of 3 Numbers - Find the Greatest Common Factor (GCF) of three numbers
- Least Common Multiple - Find the Least Common Multiple (LCM) of two numbers
- Greatest Common Factor - Find the Greatest Common Factor (GCF) of two numbers
<a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/32--48--64">What is the LCM of 32, 48 and 64? - Calculatio</a>
LCM Table
| Number 1 | Number 2 | Number 3 | LCM |
|---|---|---|---|
| 32 | 48 | 49 | 4,704 |
| 32 | 48 | 50 | 2,400 |
| 32 | 48 | 51 | 1,632 |
| 32 | 48 | 52 | 1,248 |
| 32 | 48 | 53 | 5,088 |
| 32 | 48 | 54 | 864 |
| 32 | 48 | 55 | 5,280 |
| 32 | 48 | 56 | 672 |
| 32 | 48 | 57 | 1,824 |
| 32 | 48 | 58 | 2,784 |
| 32 | 48 | 59 | 5,664 |
| 32 | 48 | 60 | 480 |
| 32 | 48 | 61 | 5,856 |
| 32 | 48 | 62 | 2,976 |
| 32 | 48 | 63 | 2,016 |
| 32 | 48 | 64 | 192 |
| 32 | 48 | 65 | 6,240 |
| 32 | 48 | 66 | 1,056 |
| 32 | 48 | 67 | 6,432 |
| 32 | 48 | 68 | 1,632 |
| 32 | 48 | 69 | 2,208 |
| 32 | 48 | 70 | 3,360 |
| 32 | 48 | 71 | 6,816 |
| 32 | 48 | 72 | 288 |
| 32 | 48 | 73 | 7,008 |
| 32 | 48 | 74 | 3,552 |
| 32 | 48 | 75 | 2,400 |
| 32 | 48 | 76 | 1,824 |
| 32 | 48 | 77 | 7,392 |
| 32 | 48 | 78 | 1,248 |
About "Least Common Multiple of 3 Numbers" Calculator
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder