LCM of 5, 6, 7 and 8 is 840. For the numbers 5, 6, 7 and 8 the smallest common multiple among many is 840, and hence it is the LCM. LCM stands for Least Common Multiple or the Lowest common multiple also known as LCD Least Common Divisor. 1680, 2520, 3360 are also the common multiples. You can refer to Multiples.
What is LCM of 5, 6, 7 and 8
The Least Common Multiple or Lowest Common Multiple of 5, 6, 7 and 8 is 840.
How to Find LCM of 5, 6, 7 and 8?
LCM of 5, 6, 7 and 8 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 5, 6, 7 and 8 Using Prime Factorisation Method
In the Prime Factorisation method, 5, 6, 7 and 8 can be expressed as;
5 = 1 × 5
6 = 2 × 3
7 = 1 × 7
8 = 2 × 2 × 2
The product of common and uncommon prime divisors of 5, 6, 7 and 8 forms the LCM.
LCM (5, 6, 7 and 8) = 2 × 2 × 2 × 3 × 5 × 7 = 840
LCM of 5, 6, 7 and 8 Using Division Method
In the Division Method, the 5, 6, 7 and 8 numbers are divided by prime divisors and the product of these prime divisors will be the LCM.
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LCM (5, 6, 7 and 8) = 2 × 2 × 2 × 3 × 5 × 7 = 840
LCM of 5, 6, 7 and 8 Using Listing the Multiples
By listing all the multiples of 5, 6, 7 and 8, we can identify the first common multiple, which is the LCM. Below is the list of multiples for 5, 6, 7 and 8
Multiples of 5
5, 10, 15, …, 360, 365, ..385, …, 495, 500, .. 600, … 700, …, 800, .. 830, 835, 840, 845, 850
Multiples of 6
6, 12, 18, .. 60, 66, 72, 78, 84, …, 240, 246, 252, 258, ..390, 396, …, 528, 534,.. 768, 774,.. 816, 822, 828, 834, 840, 846, 852
Multiples of 7
7, 14, 21, … 329, 336, 343, … 497, 504, 511, 518, …672, 679, 686, .. 791, 798, 805, .., 826, 833, 840, 847, 854
Multiples of 8
8, 16, 24, 32, … 240, 248, 256, 264,.., 440, 448, 456, .., 632, 640, 648, .. 784, 792, .. 832, 840, 848, 856
LCM (5, 6, 7 and 8) = 840
Related Articles
- LCM
- HCF and LCM
- LCM Formula
- LCM Calculator
- Prime Factorization and Division method
- LCM with Examples
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by 5, 6, 7 and 8?
Answer: 840 is the smallest number that is divisible by 5, 6, 7 and 8.
What is the LCM of 3 and 840?
Answer: LCM of 3 and 840 is 840.
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