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## What are the multiples of 30?

A positive integer is a multiple of 30 when it can be divided by 30; this means that its division by 30 gives an integer quotient and zero remainder.
If a natural number m is a multiple of 30, it exists an integer q such that: m/30=q and 30*q=m.
2; 3; 5; 6; 10; 15 are divisors of 30, if a number is a multiple of 30 then that number is also a multiple of 2; 3; 5; 6; 10 and 15.
If a number is a multiple of 30 then it must meet one of the following conditions:
- if a natural number is divisible by 2 and 15 then that number is a multiple of 30;
- if a natural number is divisible by 3 and 10 then that number is a multiple of 30;
- if a natural number is divisible by 5 and 6 then that number is a multiple of 30;

Example: 180 is a multiple of 30 'because 180 is divisible by 2 and 15, 180/2=90 and 180/15=12'.
Here are some multiples of 30 greater than 0:
Multiples of 30 less than 1000:
30; 60; 90; 120; 150; 180; 210; 240; 270; 300; 330; 360; 390; 420; 450; 480; 510; 540; 570; 600; 630; 660; 690; 720; 750; 780; 810; 840; 870; 900; 930; 990.

Multiples of 30 up to 1000 and less than 2000:
1020; 1050; 1080; 1110; 1140; 1170; 1200; 1230; 1260; 1290; 1320; 1350; 1380; 1410; 1440; 1470; 1500; 1530; 1560; 1590; 1620; 1650; 1680; 1710; 1740; 1770; 1800; 1830; 1860; 1890; 1920; 1950; 1980.

Multiples of 30 between 2000 and 3000:
2010; 2040; 2070; 2100; 2130; 2160; 2190; 2220; 2250; 2280; 2310; 2340; 2370; 2400; 2430; 2460; 2490; 2520; 2550; 2580; 2610; 2640; 2670; 2700; 2730; 2760; 2790; 2820; 2850; 2880; 2910; 2940; 2970; 3000.

Multiples of 29 up to 4000 and less than 5000:
4020; 4050; 4080; 4110; 4140; 4170; 4200; 4230; 4260; 4290; 4320; 4350; 4380; 4410; 4440; 4470; 4500; 4530; 4560; 4590; 4620; 4650; 4680; 4710; 4740; 4770; 4800; 4830; 4860; 4890; 4920; 4950; 4980.

What is the least common multiple of 20 and 30?
The least common multiple of 20 and 30 is 60.

What is the least common multiple of 12 and 30?
The least common multiple of 12 and 30 is 60.