Expanding disk inside Hyper-V using LVM

If you want to do this without GUI tools, you can use parted.

On my system, I was expanding the root filesystem (which was on dev/sda3) from 128GB to 160GB. Adjust the examples below depending on your setup. All the commands must be run as root (sudo -i to login as root).

Beforehand, I was at 95% usage:

# df -h
Filesystem                         Size  Used Avail Use% Mounted on
/dev/mapper/ubuntu--vg-ubuntu--lv  124G  113G  6.3G  95% /

With Gen2 virtual machines, everything can be done online, while the guest OS is running, and without rebooting. Each step is almost instantaneous.

First, expand the virtual disk using the Hyper-V GUI or CLI tools (easiest way is to open the VM's settings, select the hard drive under the SCSI controller, then choose "Edit" then "Expand").

Next, you need to tell Ubuntu to rescan the block device, in this case sda:

# echo 1 > /sys/block/sda/device/rescan

Next, run parted and choose p for print. It should recognize that the partition table isn't using the full space and ask whether you want to fix it, so choose Fix at this point.

# parted /dev/sda
GNU Parted 3.2
Using /dev/sda
Welcome to GNU Parted! Type 'help' to view a list of commands.
(parted) p
Warning: Not all of the space available to /dev/sda appears to be used, you can fix the GPT to use all of the space (an
extra 69206016 blocks) or continue with the current setting?
Fix/Ignore? Fix
Model: Msft Virtual Disk (scsi)
Disk /dev/sda: 172GB
Sector size (logical/physical): 512B/4096B
Partition Table: gpt
Disk Flags:

Number  Start   End     Size    File system  Name  Flags
 1      1049kB  538MB   537MB   fat32              boot, esp
 2      538MB   1612MB  1074MB  ext4
 3      1612MB  136GB   135GB

Now you need to actually expand the partition. While still in parted, enter the resizepart command to accomplish this. In my case, since I'm expanding sda3 I tell it to resize partition 3 to 100% of available space. Again, adjust the command for your setup.

(parted) resizepart 3 100%
(parted) p
Model: Msft Virtual Disk (scsi)
Disk /dev/sda: 172GB
Sector size (logical/physical): 512B/4096B
Partition Table: gpt
Disk Flags:

Number  Start   End     Size    File system  Name  Flags
 1      1049kB  538MB   537MB   fat32              boot, esp
 2      538MB   1612MB  1074MB  ext4
 3      1612MB  172GB   170GB

(parted) quit

Type quit to exit parted.

If you're using LVM, you now need to tell it to expand the physical volume. pvs shows the info on your physical volumes; use pvresize to expand it. With no parameters given, it will use all available space.

# pvs
  PV         VG        Fmt  Attr PSize    PFree
  /dev/sda3  ubuntu-vg lvm2 a--  <125.50g    0
# pvresize /dev/sda3
  Physical volume "/dev/sda3" changed
  1 physical volume(s) resized / 0 physical volume(s) not resized
# pvs
  PV         VG        Fmt  Attr PSize    PFree
  /dev/sda3  ubuntu-vg lvm2 a--  <158.50g 33.00g

Now, you need to expand the logical volume, as well as the filesystem itself. lvextend with the -r switch will do both at once, assuming you're using a filesystem it knows about such as ext3/4.

# lvs
  LV        VG        Attr       LSize    Pool Origin Data%  Meta%  Move Log Cpy%Sync Convert
  ubuntu-lv ubuntu-vg -wi-ao---- <125.50g

# lvextend -l +100%FREE -r /dev/mapper/ubuntu--vg-ubuntu--lv
  Size of logical volume ubuntu-vg/ubuntu-lv changed from <125.50 GiB (32127 extents) to <158.50 GiB (40575 extents).
  Logical volume ubuntu-vg/ubuntu-lv successfully resized.
resize2fs 1.44.1 (24-Mar-2018)
Filesystem at /dev/mapper/ubuntu--vg-ubuntu--lv is mounted on /; on-line resizing required
old_desc_blocks = 16, new_desc_blocks = 20
The filesystem on /dev/mapper/ubuntu--vg-ubuntu--lv is now 41548800 (4k) blocks long.

That's it! Now verify that the filesystem sees the extra space:

# df -h
Filesystem                         Size  Used Avail Use% Mounted on
/dev/mapper/ubuntu--vg-ubuntu--lv  156G  113G   38G  76% /

If you're not using LVM, you can replace the pvresize/lvextend steps with resize2fs instead.

This article on Teknophiles has some more details on this process along with screenshots of the Hyper-V tools.

As of 2019, I was having some issues trying to resize a Ubuntu 18.04 V.M. running on Hyper-V. Installing gparted: sudo apt install gparted, running it: sudo gparted and going through the resizing process on the application's GUI solved my problem.

gparted GUI aid: https://youtu.be/cDgUwWkvuIY?t=330

EDIT: Apparently, this still works as far as Jan/2021 as this answer got upvotes recently.

You use gparted to resize partitions. In 12.04 you will need to boot from the livecd and run it from there as it can not resize partitions that are mounted. In later releases, it can grow many partitions while they are mounted. This will only give LVM more space to allocate to logical volumes. If you want to grow a logical volume, you can run for instance lvresize -L 30g ubuntu-vg/root to increase the size of your root lv to 30g. Then you need to tell the filesystem to use that new space, which you can do with resize2fs /dev/ubuntu-vg/root, assuming you are using the default ext4 filesystem. These two latter steps can be performed online rather than booting from other media. You can also specify 100% instead of 30g to lvresize to use all available space, but it kind of defeats the purpose of using LVM in the first place to allocate all space to one logical volume, since you don't have any free space for creating snapshots, new logical volumes, or growing some volumes later.